Question

Which equation, when graphed, has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16)?

f(x) = –(x – 2)(x – 4)
f(x) = –(x + 2)(x + 4)
f(x) = –2(x – 2)(x – 4)
f(x) = –2(x + 2)(x + 4)

Answer 1

Plug x = 0 into the general form k(x − 2)(x − 4): f(0) = k(−2)(−4) = 8k.
We need 8k = −16, so k = −2.

Thus the correct equation is f(x) = −2(x − 2)(x − 4).