quick write write down the 2 formats we have learned for quadratics under each format, write down...

Quick Write

• Write down the 2 formats we have learned for quadratics

• Under each format, write down all the things you can get from that format.

Review

• Multiply these together:

( 6)( 4)x x 2 2 24x x

INTERCEPT FORMAT

Section 4-2

Objectives

• I can find the solutions, axis of symmetry, and vertex point from Intercept Format

• I can graph a quadratic from Intercept Format

• I can convert Intercept Format to Standard Format

Intercept Format

( )( )y a x p x q p and q are the x-intercepts

AOS:2

p qx

a > 0 Opens Up

a < 0 Opens Down

Graphing Steps

• Find p and q

• Calculate AOS

• Calculate Vertex using AOS x-value

• Calculate y-intercept Let x = 0

2

p qx

EXAMPLE 3 Graph a quadratic function in intercept form

Graph y = 2(x + 3) (x – 1).

SOLUTION

STEP 1 Identify the x - intercepts. Because p = – 3 and q = 1, the x - intercepts occur at the points (– 3, 0) and (1, 0).

STEP 2 Find the coordinates of the vertex.

x = p + q2

– 3 + 1 2

= – 1=

y = 2(– 1 + 3)(– 1 – 1) = – 8

EXAMPLE 3 Graph a quadratic function in intercept form

STEP 3 Draw a parabola through the vertex and the points where the x - intercepts occur.

GUIDED PRACTICE

Graph the function. Label the vertex, axis of symmetry, and x - intercepts.

5. y = (x – 3) (x – 7)

SOLUTION

STEP 1 Identify the x - intercepts. Because p = 3 and q = 7, the x - intercepts occur at the points (3, 0) and (7, 0).

STEP 2 Find the coordinates of the vertex.

x = p + q2

3 + 7 2

= 5=

y = (5 – 3) (5 – 7) = – 4

So the vertex is (5, – 4)

GUIDED PRACTICE for Examples 3 and 4

STEP 3 Draw a parabola through the vertex and the points where the x - intercepts occur.

GUIDED PRACTICE for Examples 3 and 4

7. y = – (x + 1) (x – 5)

SOLUTION

STEP 1 Identify the x - intercepts. Because p = – 1 and q = 5, the x - intercepts occur at the points (– 1, 0) and (5, 0).

STEP 2 Find the coordinates of the vertex.

x = p + q2

– 1 + 5 2

= 2=

y = – (2 + 3)(2 – 1) = 9

So the vertex is (2, 9)

GUIDED PRACTICE for Examples 3 and 4

STEP 3 Draw a parabola through the vertex and the points where the x - intercepts occur.

EXAMPLE 5 Change from intercept form to standard form

Write y = – 2 (x + 5) (x – 8) in standard form.

y = – 2 (x + 5) (x – 8) Write original function.

= – 2 (x2 – 8x + 5x – 40) Multiply using FOIL.

= – 2 (x2 – 3x – 40) Combine like terms.

= – 2x2 + 6x + 80 Distributive property

GUIDED PRACTICE for Examples 5 and 6

Write the quadratic function in standard form.9. y = – (x – 2) (x – 7)

y = – (x – 2) (x – 7) Write original function.

= – (x2 – 7x – 2x + 14) Multiply using FOIL.

= – (x2 – 9x + 14) Combine like terms.

= – x2 + 9x – 14 Distributive property

GUIDED PRACTICE for Examples 5 and 6

12. y = – 7(x – 6) (x + 1)

y = – 7(x – 6) (x + 1) Write original function.

= – 7(x2 + x – 6x – 6) Multiply using FOIL.

= – 7(x2 – 5x – 6) Combine like terms.

= – 7x2 + 35x + 42 Distributive property