Question

Which statements are true about the graph of the function f(x) = 6x – 4 + x2?

Check all that apply.

The vertex form of the function is f(x) = (x – 2)2 + 2.
The vertex of the function is (–3, –13).
The axis of symmetry for the function is x = 3.
The graph increases over the interval (–3, ).
The function does not cross the x-axis.v

Answer 1

Write the function as
f(x) = x² + 6x - 4

Note that
x² + 6x = (x + 3)² - 9

Therefore
f(x) = (x 3)² - 9 - 4
= (x + 3)² - 13

The vertex is at (-3, -13)., and the curve opens upward.
The axis of symmetry is x = -3.

Answer:
The vertex of the function is (-3, 13).
The graph increases over the interval (-3, -∞)