# Identifying Quadratic Functions Lesson 8 1 What does

- Slides: 68

Identifying Quadratic Functions Lesson 8 -1

What does a quadratic equation (or function) look like? •

Example 1: Tell whether the equation (or function) is quadratic. •

Example 2: Tell whether the equation (or function) is quadratic continued. •

Example 3: Tell whether the equation (or function) is quadratic continued. •

Your Turn: Tell whether the function is quadratic. •

Example 4: Graph using a table of values x -2 8 -1 2 0 0 1 2 2 8

Example 5: Graph using a table of values x -2 -8 -1 -2 0 0 1 -2 2 -8

Your turn: Graph using a table of values. • x -2 6 -1 3 0 2 1 3 2 6

Your turn: Graph using a table of values. • x -2 -11 -1 -2 0 1 1 -2 2 -11

Example 6: Tell whether the graph of each quadratic function opens upward or downward. •

Example 7: Identify the vertex of the parabola. Then state the maximum or minimum value. 1) What is the vertex? 2) Is it a maximum or minimum? 3) What is the maximum value or the minimum value?

Example 8: Identify the vertex of the parabola. Then state the maximum or minimum value. 1) What is the vertex? 2) Is it a maximum or minimum? 3) What is the maximum value or the minimum value?

Domain and range of a quadratic function.

Domain and range of a quadratic function.

Recap… •

Recap… •

Homework • Page 527 (26, 28, 30 – 38 all)

Characteristics of Quadratic Functions Lesson 8 -2

Example 1: Finding zeros of quadratic functions from a graph. • A zero of a function is an x-value that makes the function equal to 0. • In other words, the zero of a function is the x-intercept – where the graph crosses the x-axis – of the function.

Example 2: Finding zeros of quadratic functions from a graph. • A zero of a function is an x-value that makes the function equal to 0. • In other words, the zero of a function is the x-intercept – where the graph crosses the x-axis – of the function.

Example 3: Finding zeros of quadratic functions from a graph.

Example 4: Finding zeros of quadratic functions from a graph. 1. To see what the zeros are in the graph, see where the parabola crosses the xaxis. . 2. The parabola does NOT cross the x-axis!!! 3. So, there are no zeros of the function.

Finding the axis of symmetry. • The axis of symmetry is a vertical line that divides the parabola into two symmetrical sides. • The axis of symmetry passes through the vertex. We are going to use the zeros to find the axis of symmetry.

Example 5: Find the axis of symmetry of the parabola by using zeros.

Example 6: Find the axis of symmetry of the parabola by using zeros.

Formula for computing the axis of symmetry. • You can use this formula if there are no zeros or the zeros are hard to identify from a graph. This formula works for all quadratic functions.

Example 7: Find the axis of symmetry by using the formula. •

Example 8: Find the axis of symmetry by using the formula. •

Practice (Still part of notes). • Page 535 (3 -6, 8, 9, 12)

Finding the vertex of a parabola • Since we know how to find the axis of symmetry, we can now find the vertex of a parabola using the following steps. 1. Find the axis of symmetry of the parabola (x =). 2. Plug in the x-value into the equation to find the y-value. 3. Write the vertex as an ordered pair.

Example 9: Find the vertex of the parabola. •

Example 9 Continued: Find the vertex of the parabola. •

Example 9 Continued: Find the vertex of the parabola. •

Example 10: Find the vertex of the parabola. •

Example 10 Continued: Find the vertex of the parabola. •

Homework • Page 536 (19 -23, 25, 26, 29 -31)

Transforming Quadratic Functions Lesson 8 -4

The basics… •

• The bigger the number, the skinnier the parabola. • The smaller the number, the fatter the parabola.

Example 1: Order the functions from skinniest to fattest. •

Vertical Translations

Recap… •

Homework • Page 549 (10 -17) • Page 553 (1 -16, 21 -24) (I know it says quiz at the top, but this is your study guide for the test!)

Solving Quadratic Equations by Factoring Lesson 8 -6

Remember Factoring? •

Example 1: Solving quadratics by factoring. •

Example 1: Solving quadratics by factoring continued. •

Example 2: •

Example 3: •

Example 4: •

Example 4 Continued: •

Example 5: •

Example 6: • 2

Homework • Page 565 (2 -18)

Solving Quadratic Equations by Using Square Roots Lesson 8 -7

Square Roots • Every positive real number has two square roots. Positive Square root of 9 Negative Square root of 9 Positive and negative Square roots of 9

Example 1: •

Example 2: •

Example 3: •

Example 4: •

Example 4: •

Homework • Page 571 (18 -34 even)

- Lesson 8-1 identifying quadratic functions
- 8-1 identifying quadratic functions
- 9-1 identifying quadratic functions
- Identify and representing functions
- Adjective
- Adjective clause identification
- Identify the essential
- 8-2 characteristics of quadratic functions
- Narrowest graph example
- 8-3 transformations of quadratic functions
- Quadratic inequality graph example
- How can you identify a linear function
- Polynomial function form
- Identifying even and odd functions
- Linear and nonlinear tables
- 5-1 identifying linear functions answer key
- Lesson 4.4 identifying movable joints
- Chapter 13 lesson 1 identifying the substance of the gene
- Solving quadratic equations by elimination
- Quadratic equation examples
- Vertex form of a quadratic
- How to graph quadratic functions using transformations
- Graph using transformations
- Irrational equation
- Graphsketch
- Introduction to quadratic functions
- How to know if an equation is linear or quadratic
- Maximum and minimum values of quadratic functions
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- Quadratic vocabulary
- Properties of quadratic functions
- Properties of quadratic functions in standard form
- Properties of quadratic graphs
- Properties of quadratic functions
- Dilation factor quadratic
- Quadratic functions and their graphs
- Crime scene factoring and quadratic functions answer key
- Polynomial in standard form
- Y^2=ax graph
- Vertex form
- Sketching graphs of quadratic functions
- What are the zeros of a quadratic function
- Vertex form from a graph
- Comparing quadratic functions
- Chapter 9 quadratic equations and functions
- Chapter 8 quadratic functions and equations answer key
- 9-1 practice graphing quadratic functions
- Vertex x coordinate
- 9-4 transforming quadratic functions
- Example of narrowest graph
- 9-1 graphing quadratic functions
- Which of the quadratic functions has the narrowest graph?
- How to find the min or max value of a quadratic function
- Quadratic fucntion
- Standard form from graph
- Absolute vs relative maximum
- Linear and quadratic functions and modeling
- What is b in quadratic function
- Using transformations to graph quadratic functions
- Translations quadratic functions
- 4-1 graphing quadratic functions
- Exploring quadratic graphs
- What is the domain of a parabola
- 9-3 graphing quadratic functions
- 9-1 graphing quadratic functions answer key
- Graphing from standard form
- Quadratic functions characteristics
- Translating quadratic functions
- How to know if a graph opens up or down