Anatomy of a Quadratic Function Quadratic Form Any

  • Slides: 28
Download presentation
Anatomy of a Quadratic Function

Anatomy of a Quadratic Function

Quadratic Form Any function that can be written in the form Ax 2+Bx+C where

Quadratic Form Any function that can be written in the form Ax 2+Bx+C where a is not equal to zero. ¢ You have already been looking at quadratics ¢ Anything with an x 2 term in the equation ¢

Creating a quadratic Done by foiling ¢ Example (3 x+2)(2 x-4) ¢

Creating a quadratic Done by foiling ¢ Example (3 x+2)(2 x-4) ¢

To be a quadratic… Must have an x 2 term ¢ Must have a

To be a quadratic… Must have an x 2 term ¢ Must have a constant number not equal to zero. ¢ Proper form: Ax 2+ Bx +C ¢ Practice identifying ¢

Create the quadratic… Foil to get the quadratic, and label a, b, and c

Create the quadratic… Foil to get the quadratic, and label a, b, and c ¢ (2 x-1)(3 x+5) ¢

Foil to get the quadratic, and label a, b, and c ¢ (2 x-5)(x-2)

Foil to get the quadratic, and label a, b, and c ¢ (2 x-5)(x-2) ¢

Quadratic Function ¢ How do I know it’s a function?

Quadratic Function ¢ How do I know it’s a function?

The parabola Graph of a quadratic function is a parabola ¢ It’s the “U”

The parabola Graph of a quadratic function is a parabola ¢ It’s the “U” shape ¢ Upward opening parabola- the coefficient with the x 2 term is positive ¢

¢ Downward opening parabola- The coefficient with the x 2 term is negative

¢ Downward opening parabola- The coefficient with the x 2 term is negative

Axis of Symmetry Each parabola has an axis of symmetry ¢ Axis of symmetry-

Axis of Symmetry Each parabola has an axis of symmetry ¢ Axis of symmetry- line that divides a parabola into two parts that are mirror images of one another ¢ DO IT ¢

The parabola ¢ Vertex- lowest point or highest point on a graph

The parabola ¢ Vertex- lowest point or highest point on a graph

Max and Min Values If the parabola opens up, the min value is at

Max and Min Values If the parabola opens up, the min value is at the vertex ¢ If the parabola opens down, the max value is at the vertex ¢

¢ The axis of symmetry passes through the vertex of the parabola

¢ The axis of symmetry passes through the vertex of the parabola

Domain and Range ¢ Domain of a parabola is all real numbers

Domain and Range ¢ Domain of a parabola is all real numbers

Range of a parabola ¢ Depends on where the parabola sits…

Range of a parabola ¢ Depends on where the parabola sits…

Solving Quadratic Functions

Solving Quadratic Functions

Square Roots x 2=a where a is any number greater than or equal to

Square Roots x 2=a where a is any number greater than or equal to 0 ¢ x is called the square root of a ¢ The solution, x has two values ¢

Properties of Square Roots Positive square root is called the principal root ¢ Properties

Properties of Square Roots Positive square root is called the principal root ¢ Properties of square roots ¢

Solve just like a regular equation ¢ Follow order of operations, but leave square

Solve just like a regular equation ¢ Follow order of operations, but leave square root till the end ¢ Simplify all other ways first ¢

4 x 2 +13=253

4 x 2 +13=253

5 x 2 -19=231

5 x 2 -19=231

9(x-2)2=121

9(x-2)2=121

4(x+2)2=49

4(x+2)2=49

Warm Up! Complete this problem at the bottom of your sheet ¢ Solve 4

Warm Up! Complete this problem at the bottom of your sheet ¢ Solve 4 x 2+5=20 ¢

Solving using the Calculator Quadratic formulas can have more than one solution ¢ Because

Solving using the Calculator Quadratic formulas can have more than one solution ¢ Because a square root of a number can give a positive and negative number ¢ They can also have no solutions, or just one ¢

So how do I know if I am right? Use your calculator ¢ Solve

So how do I know if I am right? Use your calculator ¢ Solve so the entire equation is set equal to 0 ¢ Go to y= on your calculator ¢ Plug the equation into y 1 ¢ Look for the x intercepts of the graph ¢ Use the Solve key to find values ¢

Pythagorean Theorem a 2 + b 2 =c 2 ¢ Works only for right

Pythagorean Theorem a 2 + b 2 =c 2 ¢ Works only for right triangles ¢ What is a right triangle? ¢

Homework: page 286 ¢ #15, 18, 21, 24, 27, 30

Homework: page 286 ¢ #15, 18, 21, 24, 27, 30