Question

Identify the vertex and sketch the graph.f (x) = -2x 2 - 24x - 72

Answer 1

ANSWER

Vertex = (-6, 0) Option B

Graph:

EXPLANATION

Given:

$f(x)=-2x^2-24x-72$

Desired Outcome:

Vertex and graph

Rewrite the equation in vertex form

$y=a(x-h)^2+k$

where:

(h, k) is the vertex.

Now, determine the vertex of the equation

$\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-(-24)}{2(-2)} \\ h=\frac{24}{-4} \\ h=-6 \end{gathered}$$k=-\frac{D}{4a}$

Let's determine the value of D

$\begin{gathered} D=b^2-4ac \\ D=(-24)^2-4(-2)(-72) \\ D=576-576 \\ D=0 \end{gathered}$

Now,

$\begin{gathered} k=-\frac{D}{4a} \\ k=-\frac{0}{4(-2)} \\ k=\frac{0}{8} \\ k=0 \end{gathered}$

Therefore, the vertex (h, k) = (-6, 0) and when we plot this on a graph, we have:

Hence, the correct option is B.