Question

Find the vertex for the parabola given by the function ƒ(x) = −3x^2 − 6x.

A) (1, 3)
B) (−1, 3)
C) (−1/2, 2)
D) (−1/2, 3)

Answer 1

B) (−1, 3)

Explanation:

The standard form of a quadratic function is

y = ax² + bx + c

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

In your equation, ƒ(x) = −3x² − 6x

a = -3; b = -6; c = 0

Calculate h

h = -(-6)/2(-3)]

h = 6/(-6)

h = -1

Calculate k

k = -3(-1)² -6(-1)

k = -3 + 6

k = 3

So, h = -1, k = 3, a = -3

The vertex form of the equation is f(x) = -3(x + 1)² + 3.

The vertex is at (-1, 3).

The figure below shows the graph of ƒ(x) = −3x² − 6x with the vertex

at (-1, 3).