Question

The zeros of a function are at x = -5 and x=9. Which of the following is an equivalent expression that will reveal the vertex?

f(x) = x2 + 41 – 45
f(x) = x2 - 4x – 45
f(t) = (2 – 2)2 – 49
f(3) = (x+2)2 - 49

Answer 1

f(x) = x² + 4x - 45. That is the 2nd answer given.

Explanation:

If the zeros of a function are x = -5 and x = 9, that means

f(x) = 0 when x = -5 or when x = 9

So we can try factoring f(x) as f(x) = {x - (-5)} * (x - 9)

f(x) = (x + 5)(x-9)

f(x) = x² + 4x - 45

That is the 2nd answer given.