Question

Find the quadratic function whose graph is shown to the right. Write the functionin the form f(x) = a(x – h)2 + k.f(x)=0(Do not simplify.)

Answer 1

`\begin{gathered} f(x)=a(x-h)^2_{}+k \\ y=a(x-h)^2+k \\ From\text{ the graph:} \\ h=-3,k=11,x=0,y=2 \\ Substitute\text{ the variables into the standard equation} \\ 2=a(0-(-3))^2+11 \\ 2=a(3)^2+11 \\ 2=9a^{}+11 \\ \text{Rearrange the equation, we have:} \\ 9a^{}=2-11\Rightarrow9a=-9 \\ a=-1 \\ Substitute\text{ the variables into the standard equation} \\ f(x)=-(x-(-3))^2+11 \\ f(x)=-(x+3)^2+11 \\ f(x)=-(x+3)(x+3)+11 \\ f(x)=-(x^2+6x+9)+11 \\ f(x)=-x^2-6x-9+11 \\ f(x)=-x^2-6x+2 \end{gathered}`