Question

Hello! I need some assistance with this homework question, pleaseQ12

Answer 1

A(-1,4) and B(2,0)

Explanation:

The quadratic parabola equation is represented as;

`\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex of the parabola} \end{gathered}`

Therefore, if the given vertex (2,-5) and the other given point (-1,-1), substitute into the equation and solve for the constant ''a'':

`\begin{gathered} -1=a(-1-2)^2-5 \\ -1=9a-5 \\ 9a=4 \\ a=(4)/(9) \end{gathered}`

Hence, the equation for the parabola:

`f(x)=(4)/(9)(x-2)^2-5`

Now, for the line since it is a horizontal line, the equation would be:

`g(x)=5`

Then, for (f+g)(x):

`\begin{gathered} (f+g)(x)=(4)/(9)(x-2)^2-5+5 \\ (f+g)(x)=(4)/(9)(x-2)^2 \end{gathered}`

Then, the graph for the composite function and the points that lie on the graph:

A(-1,4) and B(2,0)