Answer
See below
Work Step by Step
The function is in the form $a(x-h)^2+k$. We know that the axis of symmetry is $\frac{p+q}{2}$.
The first function is $y=- 0.5(x - 6)+ 18$
where $a=-0.5\\h=6\\k=18$
The vertex of this function is $(h,k)=(6,18)$
The second function is $y=- 1.17(x - 6)+ 42$
where $a=-1.17\\h=6\\k=42$
The vertex of this function is $(h,k)=(6,42)$
Hence, the maximum value of the first function is $y=18$. The maximum value of the second function is $y=42$.
Since $y=k$ is the maximum value of the function, $k$ affects the maximum heights of the jumps on the two pogo sticks. Other constants ($a$ and $h$) do not affect the maximum heights of the jumps.
