Answer:
[tex]\begin{gathered} a=\frac{1}{7} \\ h(x)=\frac{1}{7}(x-7)^2-3 \end{gathered}[/tex]
Step-by-step explanation:
We know that the ''a'' coefficient represents a stretch or compression, if it is between 0 and 1, it is a horizontal stretch:
[tex]\begin{gathered} h(x)=a(x-7)^2-3 \\ \text{ Since we know that at x=0, h(x)=4} \\ 4=a(0-7)^2-3 \\ 4=49a-3 \\ 49a=7 \\ a=\frac{7}{49} \\ a=\frac{1}{7} \end{gathered}[/tex]
Therefore, the equation for the function shown is:
[tex]h(x)=\frac{1}{7}(x-7)^2-3[/tex]
