What are the three forms a quadratic equation can be written in? Vertex Standard Factored

9.5 WRITING QUADRATIC

EQUATIONS – THREE FORMS

What are the three forms a quadratic equation can be written in?Vertex

Standard

Factored

2y a x h k

2y ax bx c

1 2y a x r x r

Yesterday, we were able to graph all three. We are also able to convert between the three equations algebraically most of the time.

Converting into vertex form requires the coordinates of the .

Converting into factored form requires the .

Converting into standard form requires and combining like terms. 

In each form the is the same!

vertex

x-intercepts or factoring

FOIL

a

1. Given the quadratic equation

a. Write the equation in standard form.

b. Write the equation in vertex form.

f x 2 x 3 x 5

2. Given the quadratic equation

a. Write the equation in factored form.

b. Write the equation in vertex form.

f x 3x2 18x 48

3. Given the quadratic equation

a. Write the equation in standard form.

b. Write the equation in factored form.

f x x 3

2

2

441

4

4. Given the quadratic equation

a. Write the equation in factored form.

b. Write the equation in vertex form.

f x 1

2x2

3

2x 27