Algebra 1 Common Core Student Edition, Grade 8-9

(§^ Common Core Stat e St andards

jla

and the Discriminant

The Q uadratic Formula transform any quadratic equation in x in to an equation

o f the form (x- p)2 = q ... Derive the quadratic

formula from this form. Also A-REI.B.4b

MP 1, MP 2, MP 3, MP 4, MP 7, MP 8

Ob j ect i v es To solve quadratic equations using the quadratic formula

To find the number of solutions of a quadratic equation

Getting Ready!

You have several

ways to solve

th is problem :

graphing, making

a tab le, and

fa cto rin g. W h ich

will you u se?

Y o u r f r ie n d 's a u n t h as a b r ic k w a lk w a y in h e r b a c k y a r d. H e r plan is

to decrease the length by th e same amount she increases the width

to make a rectangular patio. She wants th e patio to have an area

of 310 f t 2. Can she build a patio to meet her plan? Explain your

reasoning.

MATHEMATICAL
PRACTICES Recan that quadratic equations can have two, one, or no real-number solutions. A
quadratic equation can never have more than two solutions.
Lesso n
^|f!r Vocab ulary

• q u ad ratic
  form u la


• discrim inant

Essent ial Und er st and ing You can find the solution(s) of any quadratic equation

using the quadratic form ula.

Key Concep t Quadratic Formula

Algebra

If ax2 + bx + c = 0, and a f 0, then

-b ± Vb2^4 ac

Example

Suppose 2x2 + 3x — 5 = 0. Then a = 2, b = 3, and c = —5. Therefore

-(3) ± V(3)2 - 4(2)(-5)

2 ( 2 )

582 Ch ap t er 9 Quadratic Functions and Equations

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