f(x) = 1/4(x + 5)^2 + 2

Question

Identify the vertex and whether the graph opens up or down.

A) (-5, 2); opens down

B) (5, 2); opens down

C) (-5, 2); opens up

D) (5, 2); opens up

Answer 1

The given equation is in the form of vertex form: f(x) = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.

Comparing the given equation f(x) = 1/4(x + 5)^2 + 2 to the vertex form, we can identify that the vertex is (-5, 2).

Since the coefficient "a" is positive (1/4), the graph opens upward.

Therefore, the correct answer is: C) (-5, 2); opens up.