Question

Quadratic Functions: Factored Form

Warm-Up Active
6
Identifying Quadratic Functions in Factored Form
A. f(x) = x2 - 118-12
B.f(x) = x2 - 4x-12
C.FX) = x2+x-12
D. f(x) = x2-x-12
Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
f(x) = (x + 2)(x-6)
f(x) = (x - 4)(x+3)
f(x) = (x - 12)(x+1)
f(x) = (x - 3)(x +4)

Answer 1

a. (x - 12)(x+1)

b. (x + 2)(x-6)

c.(x - 3)(x +4)

d.(x - 4)(x+3)

Answer 2

B, D, A, C

Explanation:

When you expand the factored form, the result is ...

(x +a)(x +b) = x^2 +(a+b)x +ab

The answer choices differ only in their middle term, so you only need to look at the x-coefficient. That is, you only need to look at the sum of the constants in the binomial terms:

f(x) = (x + 2)(x-6) ⇒ 2-6 = -4 . . . . matches B

f(x) = (x - 4)(x+3) ⇒ -4+3 = -1 . . . . matches D

f(x) = (x - 12)(x+1) ⇒ -12+1 = -11 . . . . matches A

f(x) = (x - 3)(x +4) ⇒ -3+4 = 1 . . . . matches C