Factor and Solve:1. x² - 6x – 27 = 02. 4x² - 1 = 0

Convert to Vertex Format by Completing the Square (hint: kids at the store)3. Y = 3x² - 12x + 20

Warm Up

I can write a quadratic equation given solutions from the graph

Identify the 3 forms of a quadratic equation:

Standard Format ax² + bx + c*** c is where the graph crosses the y axis ***

Vertex Format y = a(x – h)² + k*** gives the vertex (h, k) ***

Intercept Format y = a(x – p)(x – q)*** gives the roots, zeros or solutions of the graph ***

Write a quadratic equation in standard form that has the given solutions and

passes through the given point.

A quadratic equation has roots of {-1, -3} and passes though (-4, 3).

Which quadratic format is best to use given the roots of the graph?

INTERCEPT FORM y=a(x – p)(x – q)

y = a (x - p)(x - q)

y = a (x + 1)(x + 3 ) Substitute -1 for p and -3 for q

A quadratic equation has roots of {-1, -3} and passes though (-4, 3).

Use the other given point (-4, 3) to find A

Step 1:

Step 2:

3 = a (-4+1)(-4 + 3)

Replace y With 3

Replace x With -4

A quadratic equation has roots of {-1, -3} and passes though (-4, 3).

3 = a(-3)(-1) Simplify3 = 3a Simplify1 = a Solve for a

3 = a (-4+1)(-4 + 3)

Step 3:

Step 4:

The quadratic equation for the parabola in intercept form

y = 1(x + 1)(x + 3)

To find the equation for the parabola in standard form you will need to FOIL.

1(x² + 3x + 1x -4) FOIL

1(x² + 4x - 4) Simplify

x² + 4x - 4 Distribute

Yo u r Tu r n

Write an quadratic equation in standard format: ax² + bx + c = 0

that has the given solutions and passes through the given point.

Example:A quadratic equation has roots of {-1, 4} and passes though (3, 2).