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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