Question

Part A: Show work to complete the square of the function.Part B: Identify the vertex of the function.Part C: Explain how to determine the maximum or minimum value of the function.

Answer 1

Part A:

Given function is

`y=-3x^2-6x-5`

While comparing the above function with the square of the function

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

then, we have

`\begin{gathered} y=-3x^2-6x-5=a(x-h)^2+k \\ =-3(x-h)^2+k \\ =-3(x^2-2hx+h^2)+k \\ =-3x^2+6hx-3h^2+k \\ =-3x^2+6hx+(k-3h^2) \end{gathered}`

while comparing the above equations,

`\begin{gathered} y=-3x^2-6x-5=-3x^2+6hx+(k-3h^2) \\ \therefore a=-3\text{ } \\ \Rightarrow-6=6h \\ \therefore h=-1 \\ \Rightarrow-5=k-3h^2 \\ -5+3(-1)^2=k \\ k=-5+3 \\ \therefore k=-2 \end{gathered}`

therefore, the square of the function will be

`\begin{gathered} \text{substituting a=-3 , h=-1 and k=-2 in Square of the function} \\ y=a(x-h)^2+k \\ \therefore y=-3(x+1)^2-2 \end{gathered}`