Question

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

Answer 1

Vertex = (-6, 0) Option B

Graph:

Step-by-step 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=(-b)/(2a) \\ h=(-(-24))/(2(-2)) \\ h=(24)/(-4) \\ h=-6 \end{gathered}`
`k=-(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=-(D)/(4a) \\ k=-(0)/(4(-2)) \\ k=(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.