ANSWER
Vertex = (-6, 0) Option B
Graph:
EXPLANATION
Given:
[tex]f(x)=-2x^2-24x-72[/tex]
Desired Outcome:
Vertex and graph
Rewrite the equation in vertex form
[tex]y=a(x-h)^2+k[/tex]
where:
(h, k) is the vertex.
Now, determine the vertex of the equation
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-(-24)}{2(-2)} \\ h=\frac{24}{-4} \\ h=-6 \end{gathered}[/tex][tex]k=-\frac{D}{4a}[/tex]
Let's determine the value of D
[tex]\begin{gathered} D=b^2-4ac \\ D=(-24)^2-4(-2)(-72) \\ D=576-576 \\ D=0 \end{gathered}[/tex]
Now,
[tex]\begin{gathered} k=-\frac{D}{4a} \\ k=-\frac{0}{4(-2)} \\ k=\frac{0}{8} \\ k=0 \end{gathered}[/tex]
Therefore, the vertex (h, k) = (-6, 0) and when we plot this on a graph, we have:
Hence, the correct option is B.
