Solving Quadratics Quadratic Formula Discriminant Nature of the
![Solving Quadratics Quadratic Formula Discriminant – Nature of the Roots Solving Quadratics Quadratic Formula Discriminant – Nature of the Roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-1.jpg)
![Warm Up – Question 1 o Given o and o find an expression for Warm Up – Question 1 o Given o and o find an expression for](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-2.jpg)
![Warm Up Answer Warm Up Answer](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-3.jpg)
![Warm Up – Question 2 o Given a) b) Warm Up – Question 2 o Given a) b)](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-4.jpg)
![](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-5.jpg)
![](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-6.jpg)
![Solve by Quadratic Formula Solve by Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-7.jpg)
![Derive the Quadratic Formula by Completing the Square Derive the Quadratic Formula by Completing the Square](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-8.jpg)
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-9.jpg)
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-10.jpg)
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-11.jpg)
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-12.jpg)
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-13.jpg)
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-14.jpg)
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-15.jpg)
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-16.jpg)
![The Discriminant The nature of the roots The Discriminant The nature of the roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-17.jpg)
![The Discriminant o o It comes from the quadratic formula. = The Discriminant o o It comes from the quadratic formula. =](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-18.jpg)
![o When you apply the quadratic formula to any quadratic equation, you will find o When you apply the quadratic formula to any quadratic equation, you will find](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-19.jpg)
![Solutions of a Quadratic Equation o If Solutions of a Quadratic Equation o If](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-20.jpg)
![Real Numbers (ℝ) Rational Numbers (ℚ) Integers (ℤ) Whole Numbers Natural Numbers (ℕ) 1, Real Numbers (ℝ) Rational Numbers (ℚ) Integers (ℤ) Whole Numbers Natural Numbers (ℕ) 1,](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-21.jpg)
![Find the Discriminant and Describe its Roots. o Nature of the Roots Find the Discriminant and Describe its Roots. o Nature of the Roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-22.jpg)
![Find the Discriminant and Describe its Roots. o Nature of the Roots Find the Discriminant and Describe its Roots. o Nature of the Roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-23.jpg)
![Find the Discriminant and Describe its Roots o Nature of the Roots Find the Discriminant and Describe its Roots o Nature of the Roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-24.jpg)
![Graphs of Polynomial Functions Graphs of Polynomial Functions](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-25.jpg)
![Explore – Look at the relationship between the degree & sign of the leading Explore – Look at the relationship between the degree & sign of the leading](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-26.jpg)
![Explore – Look at the relationship between the degree & sign of the leading Explore – Look at the relationship between the degree & sign of the leading](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-27.jpg)
![Explore – Look at the relationship between the degree & sign of the leading Explore – Look at the relationship between the degree & sign of the leading](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-28.jpg)
![Continuous Function o A function is continuous if its graph can be drawn with Continuous Function o A function is continuous if its graph can be drawn with](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-29.jpg)
![Polynomial Function o Polynomial Functions have continuous graphs with smooth rounded turns. o Written: Polynomial Function o Polynomial Functions have continuous graphs with smooth rounded turns. o Written:](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-30.jpg)
![Explore using graphing Calculator Describe graph as S or W shaped. Function Degree # Explore using graphing Calculator Describe graph as S or W shaped. Function Degree #](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-31.jpg)
![Generalizations? o The number of turns is one less than the degree. o Even Generalizations? o The number of turns is one less than the degree. o Even](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-32.jpg)
![Describe the Shape and Number of Turns. Describe the Shape and Number of Turns.](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-33.jpg)
![Let’s explore some more…. we might need to revise our generalization. o Take a Let’s explore some more…. we might need to revise our generalization. o Take a](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-34.jpg)
![Lead Coefficient Test When n is odd Lead Coefficient is Positive: (an >0), the Lead Coefficient Test When n is odd Lead Coefficient is Positive: (an >0), the](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-35.jpg)
![Lead Coefficient Test When n is even Lead Coefficient is Positive: (an >0), the Lead Coefficient Test When n is even Lead Coefficient is Positive: (an >0), the](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-36.jpg)
![Leading Coefficient: an End Behavior - a>0 a<0 left right n - even n Leading Coefficient: an End Behavior - a>0 a<0 left right n - even n](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-37.jpg)
![Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-38.jpg)
![Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-39.jpg)
![Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-40.jpg)
![Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-41.jpg)
![A polynomial function (f) of degree n , the following are true o The A polynomial function (f) of degree n , the following are true o The](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-42.jpg)
![Local Max / Min (in terms of y) Increasing / Decreasing (in terms of Local Max / Min (in terms of y) Increasing / Decreasing (in terms of](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-43.jpg)
![Local Max / Min (in terms of y) Increasing / Decreasing (in terms of Local Max / Min (in terms of y) Increasing / Decreasing (in terms of](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-44.jpg)
![Approximate any local maxima or minima to the nearest tenth. Find the intervals over Approximate any local maxima or minima to the nearest tenth. Find the intervals over](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-45.jpg)
![Find the Zeros of the polynomial function below and sketch on the graph: Find the Zeros of the polynomial function below and sketch on the graph:](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-46.jpg)
![Find the Zeros of the polynomial function below and sketch on the graph: Multiplicity Find the Zeros of the polynomial function below and sketch on the graph: Multiplicity](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-47.jpg)
![Find the Zeros of the polynomial function below and sketch on the graph: Find the Zeros of the polynomial function below and sketch on the graph:](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-48.jpg)
![Find the Zeros of the polynomial function below and sketch on the graph: NO Find the Zeros of the polynomial function below and sketch on the graph: NO](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-49.jpg)
![Find the Zeros of the polynomial function below and sketch on the graph: Find the Zeros of the polynomial function below and sketch on the graph:](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-50.jpg)
- Slides: 50
![Solving Quadratics Quadratic Formula Discriminant Nature of the Roots Solving Quadratics Quadratic Formula Discriminant – Nature of the Roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-1.jpg)
Solving Quadratics Quadratic Formula Discriminant – Nature of the Roots
![Warm Up Question 1 o Given o and o find an expression for Warm Up – Question 1 o Given o and o find an expression for](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-2.jpg)
Warm Up – Question 1 o Given o and o find an expression for the composite function and state its domain restrictions.
![Warm Up Answer Warm Up Answer](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-3.jpg)
Warm Up Answer
![Warm Up Question 2 o Given a b Warm Up – Question 2 o Given a) b)](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-4.jpg)
Warm Up – Question 2 o Given a) b)
![](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-5.jpg)
![](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-6.jpg)
![Solve by Quadratic Formula Solve by Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-7.jpg)
Solve by Quadratic Formula
![Derive the Quadratic Formula by Completing the Square Derive the Quadratic Formula by Completing the Square](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-8.jpg)
Derive the Quadratic Formula by Completing the Square
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-9.jpg)
Solve using the Quadratic Formula
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-10.jpg)
Solve using the Quadratic Formula
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-11.jpg)
Solve using the Quadratic Formula
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-12.jpg)
Solve using the Quadratic Formula
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-13.jpg)
Solve using the Quadratic Formula
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-14.jpg)
Solve using the Quadratic Formula
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-15.jpg)
Solve using the Quadratic Formula
![Solve using the Quadratic Formula Solve using the Quadratic Formula](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-16.jpg)
Solve using the Quadratic Formula
![The Discriminant The nature of the roots The Discriminant The nature of the roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-17.jpg)
The Discriminant The nature of the roots
![The Discriminant o o It comes from the quadratic formula The Discriminant o o It comes from the quadratic formula. =](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-18.jpg)
The Discriminant o o It comes from the quadratic formula. =
![o When you apply the quadratic formula to any quadratic equation you will find o When you apply the quadratic formula to any quadratic equation, you will find](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-19.jpg)
o When you apply the quadratic formula to any quadratic equation, you will find that the value of b²-4 ac is either positive, negative, or 0. o The value of the discriminant is what tells us the nature of the roots (solutions) to the quadratic.
![Solutions of a Quadratic Equation o If Solutions of a Quadratic Equation o If](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-20.jpg)
Solutions of a Quadratic Equation o If
![Real Numbers ℝ Rational Numbers ℚ Integers ℤ Whole Numbers Natural Numbers ℕ 1 Real Numbers (ℝ) Rational Numbers (ℚ) Integers (ℤ) Whole Numbers Natural Numbers (ℕ) 1,](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-21.jpg)
Real Numbers (ℝ) Rational Numbers (ℚ) Integers (ℤ) Whole Numbers Natural Numbers (ℕ) 1, 2, 3, … 0, 1, 2, 3, … …-3, -2, -1, 0, 1, 2, 3, … Decimal form either terminates or repeats All rational and irrational numbers Irrational Numbers Decimal form is non-terminating and non-repeating
![Find the Discriminant and Describe its Roots o Nature of the Roots Find the Discriminant and Describe its Roots. o Nature of the Roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-22.jpg)
Find the Discriminant and Describe its Roots. o Nature of the Roots
![Find the Discriminant and Describe its Roots o Nature of the Roots Find the Discriminant and Describe its Roots. o Nature of the Roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-23.jpg)
Find the Discriminant and Describe its Roots. o Nature of the Roots
![Find the Discriminant and Describe its Roots o Nature of the Roots Find the Discriminant and Describe its Roots o Nature of the Roots](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-24.jpg)
Find the Discriminant and Describe its Roots o Nature of the Roots
![Graphs of Polynomial Functions Graphs of Polynomial Functions](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-25.jpg)
Graphs of Polynomial Functions
![Explore Look at the relationship between the degree sign of the leading Explore – Look at the relationship between the degree & sign of the leading](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-26.jpg)
Explore – Look at the relationship between the degree & sign of the leading coefficient and the right- and left-hand behavior of the graph of the function.
![Explore Look at the relationship between the degree sign of the leading Explore – Look at the relationship between the degree & sign of the leading](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-27.jpg)
Explore – Look at the relationship between the degree & sign of the leading coefficient and the right- and left-hand behavior of the graph of the function.
![Explore Look at the relationship between the degree sign of the leading Explore – Look at the relationship between the degree & sign of the leading](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-28.jpg)
Explore – Look at the relationship between the degree & sign of the leading coefficient and the right- and left-hand behavior of the graph of the function.
![Continuous Function o A function is continuous if its graph can be drawn with Continuous Function o A function is continuous if its graph can be drawn with](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-29.jpg)
Continuous Function o A function is continuous if its graph can be drawn with a pencil without lifting the pencil from the paper. Continuous Not Continuous
![Polynomial Function o Polynomial Functions have continuous graphs with smooth rounded turns o Written Polynomial Function o Polynomial Functions have continuous graphs with smooth rounded turns. o Written:](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-30.jpg)
Polynomial Function o Polynomial Functions have continuous graphs with smooth rounded turns. o Written: o Example:
![Explore using graphing Calculator Describe graph as S or W shaped Function Degree Explore using graphing Calculator Describe graph as S or W shaped. Function Degree #](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-31.jpg)
Explore using graphing Calculator Describe graph as S or W shaped. Function Degree # of U turns
![Generalizations o The number of turns is one less than the degree o Even Generalizations? o The number of turns is one less than the degree. o Even](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-32.jpg)
Generalizations? o The number of turns is one less than the degree. o Even degree → “W” Shape o Odd degree → “S” Shape
![Describe the Shape and Number of Turns Describe the Shape and Number of Turns.](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-33.jpg)
Describe the Shape and Number of Turns.
![Lets explore some more we might need to revise our generalization o Take a Let’s explore some more…. we might need to revise our generalization. o Take a](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-34.jpg)
Let’s explore some more…. we might need to revise our generalization. o Take a look at the following graph and tell me if your conjecture is correct.
![Lead Coefficient Test When n is odd Lead Coefficient is Positive an 0 the Lead Coefficient Test When n is odd Lead Coefficient is Positive: (an >0), the](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-35.jpg)
Lead Coefficient Test When n is odd Lead Coefficient is Positive: (an >0), the graph falls to the left and rises to the right Lead Coefficient is Negative: (an <0), the graph rises to the left and falls to the right
![Lead Coefficient Test When n is even Lead Coefficient is Positive an 0 the Lead Coefficient Test When n is even Lead Coefficient is Positive: (an >0), the](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-36.jpg)
Lead Coefficient Test When n is even Lead Coefficient is Positive: (an >0), the graph rises to the left and rises to the right Lead Coefficient is Negative: (an <0), the graph falls to the left and falls to the right
![Leading Coefficient an End Behavior a0 a0 left right n even n Leading Coefficient: an End Behavior - a>0 a<0 left right n - even n](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-37.jpg)
Leading Coefficient: an End Behavior - a>0 a<0 left right n - even n - odd
![Use the Leading Coeffiicent Test to describe the righthand lefthand behavior of the graph Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-38.jpg)
Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph of each polynomial function:
![Use the Leading Coeffiicent Test to describe the righthand lefthand behavior of the graph Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-39.jpg)
Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph of each polynomial function:
![Use the Leading Coeffiicent Test to describe the righthand lefthand behavior of the graph Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-40.jpg)
Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph of each polynomial function:
![Use the Leading Coeffiicent Test to describe the righthand lefthand behavior of the graph Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-41.jpg)
Use the Leading Coeffiicent Test to describe the right-hand left-hand behavior of the graph of each polynomial function:
![A polynomial function f of degree n the following are true o The A polynomial function (f) of degree n , the following are true o The](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-42.jpg)
A polynomial function (f) of degree n , the following are true o The function has at most n real zeros o The graph has at most (n-1) relative extrema (relative max/min)
![Local Max Min in terms of y Increasing Decreasing in terms of Local Max / Min (in terms of y) Increasing / Decreasing (in terms of](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-43.jpg)
Local Max / Min (in terms of y) Increasing / Decreasing (in terms of x)
![Local Max Min in terms of y Increasing Decreasing in terms of Local Max / Min (in terms of y) Increasing / Decreasing (in terms of](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-44.jpg)
Local Max / Min (in terms of y) Increasing / Decreasing (in terms of x)
![Approximate any local maxima or minima to the nearest tenth Find the intervals over Approximate any local maxima or minima to the nearest tenth. Find the intervals over](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-45.jpg)
Approximate any local maxima or minima to the nearest tenth. Find the intervals over which the function is increasing and decreasing.
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Find the Zeros of the polynomial function below and sketch on the graph:
![Find the Zeros of the polynomial function below and sketch on the graph Multiplicity Find the Zeros of the polynomial function below and sketch on the graph: Multiplicity](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-47.jpg)
Find the Zeros of the polynomial function below and sketch on the graph: Multiplicity of 2 – EVEN - Touches
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Find the Zeros of the polynomial function below and sketch on the graph:
![Find the Zeros of the polynomial function below and sketch on the graph NO Find the Zeros of the polynomial function below and sketch on the graph: NO](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-49.jpg)
Find the Zeros of the polynomial function below and sketch on the graph: NO X-INTERCEPTS!
![Find the Zeros of the polynomial function below and sketch on the graph Find the Zeros of the polynomial function below and sketch on the graph:](https://slidetodoc.com/presentation_image_h/f9b3cf7ced27c784da5e39e43ee703ca/image-50.jpg)
Find the Zeros of the polynomial function below and sketch on the graph:
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