Question

The function m is given in three equivalent forms.

Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
B
D
m(x) = 2(x+6) (x + 2)
m(x) = 2x² + 16x + 24
m(x) = 2(x+4)² - 8
Write one of the zeros.

Answer 1

m(x)=2(x+6)(x+2) is the best form to reveal the zeros.

The second choice is an un-factored quadratic, and the third choice is a quadratic in vertex form, which requires adding 8 to both sides, then dividing by 2, and taking the square root. The first choice easily reveals the roots when y=0.

Let’s find the roots:

(0)=2(x+6)(x+2)

We will distribute the 2 back into the first binomial for simplicity:

0=(2x+12)(x+2)

By the zero product property, if a•b=0, then a=0 or b=0:

2x+12=0

Solve for x:

2x=-12

x=-6

2nd binomial

x+2=0

Solve for x:

x=-2

So, the roots are x=-6, -2