Question

The function f is given in three equivalent forms.

Which form most quickly reveals the vertex?
Choose 1 answer:
f(x) = 3x^2+ 36x + 33
f(x) = 3(x+6^2-75
f(x)=3(x+1)(x+11)
What is the vertex?

Answer 1

Explanation:

Look what happens when you factor the 3 out of the first choice:

f(x) = 3x^2+ 36x + 33 = f(x) = 3(x^2+ 12x) + 11

We can "complete the square:" x^2 + 12x becomes x^2 + 12x + 36 - 36, which, in turn, becomes (x + 6)^2 - 36

so that the original f(x) becomes f(x) = 3(x + 6)^2 - 36 + 33, or

f(x) = 3(x + 6)^2 - 3

Comparing this to

f(x) =a(x - h)^2 + k reveals that h = -6 and k = -3. Thus, the vertex is at (-6, -3).