(§^ 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
am