• How do I write quadratic functions and models?

7.2 Write Quadratic Functions and Models

Example 1 Write a quadratic function in vertex formWrite a quadratic function in vertex form

Write a quadratic function whose graph has a vertex (Write a quadratic function whose graph has a vertex () ) and passes through the point (0, 5).and passes through the point (0, 5).

SolutionVertex form khxay 2

Substitute for h and k. ________ 2xay 2 3Use the point (___, ___) to find a.0 5

Substitute for x and y. ____________ 2a5 320 Solve for a.a__2

A quadratic function for the parabola is

__________________.y 2 2 2x 3

7.2 Write Quadratic Functions and Models

Checkpoint. Complete the following exercise.Checkpoint. Complete the following exercise.1. Write a quadratic function whose graph has vertex

(2, 1) and passes through the point (0, 4).

khxay 2

ay 2 2x 1

4 2 a 20 14 14 a

a43

4

3a

y 2 4

32x 1

7.2 Write Quadratic Functions and Models

Example 2 Write a quadratic function in intercept formWrite a quadratic function in intercept form

Write a quadratic function whose graph has Write a quadratic function whose graph has xx-intercepts -intercepts and and and passes through the point ( and passes through the point ().).

SolutionIntercept form qxpxay Substitute for p and q. ________ xxay 3 2

Use the point to find a.

Substitute for x and y. _____________ a4 22 32 Solve for a.a__1

A quadratic function for the parabola is

__________________.y 1 3x 2x

7.2 Write Quadratic Functions and Models

Checkpoint. Complete the following exercise.Checkpoint. Complete the following exercise.2. Write a quadratic function whose graph has x-intercepts

and 2, and passes through the point (3, 21).

qxpxay

ay 4x 2x

21 a 43 23 21 a7

a3 y 3 4x 2x

7.2 Write Quadratic Functions and Models

Example 3 Write a quadratic function in standard formWrite a quadratic function in standard form

Write a quadratic function in standard form for the parabola Write a quadratic function in standard form for the parabola that passes through the points (that passes through the points (), (0), (0), and (), and () .) .Substitute the coordinates of each point into y = ax2 + bx + c to obtain a system of three equations.

Substitute for x and y. cba _________ 26 2 2Equation 1_______________ 6 a4 cb 2Substitute for x and y. cba _________ 26 0 0Equation 2_____ 6 cSubstitute for x and y. cba _________ 2

2 2 2Equation 3_______________ 2 a4 cb 2

7.2 Write Quadratic Functions and Models

Example 3 Write a quadratic function in standard formWrite a quadratic function in standard form

Write a quadratic function in standard form for the parabola Write a quadratic function in standard form for the parabola that passes through the points (that passes through the points (), (0), (0), and (), and () .) .Rewrite the system as a system of two equations.

Substitute for c.______________ 624 ba 6Revised Equation 1__________ ba 24 12Substitute for c.______________ 624 ba 2Revised Equation 3__________ ba 24 4

7.2 Write Quadratic Functions and Models

Example 3 Write a quadratic function in standard formWrite a quadratic function in standard form

Write a quadratic function in standard form for the parabola Write a quadratic function in standard form for the parabola that passes through the points (that passes through the points (), (0), (0), and (), and () .) .Solve the system consisting of revised Equations 1 and 3.

Revised Equation 1_____________ 1224 baRevised Equation 3_____________ 424 baAdd equations._____________a8 16Solve for a.___a 2

So, ___________=_____, which means b = ___. b224 4 2

A quadratic function for the parabola is

_____________________.y 22x x2 6

7.2 Write Quadratic Functions and Models

Checkpoint. Complete the following exercise.Checkpoint. Complete the following exercise.3. Write a quadratic function in standard form for the parabola

that passes through the points andcbxaxy 2

a 5 b ca41 b2 ca91 b3 c

6 a3 b34 a8 b4

ba 2ba 21

1 ab 213b 41 c6

1cy 2x x3 1

7.2 Write Quadratic Functions and Models

Pg. 266, 7.1 #1-11