Answer: 16 units.
Step-by-step explanation:
To find the vertex, first simplify the quadratic equation into its standard form:
[tex]h(x)=-(x+1)(x-7)\\h(x)=(-x-1)(x-7)\\h(x)=-x^2+6x+7\\[/tex]
Using this formula, we can then find the axis of symmetry by using the formula S = -b/2a:
[tex]S=\frac{-6}{-2}[/tex]
The axis of symmetry lies on x = 3.
You can then substitute x for 3 in the equation to find the vertex of the parabola:
[tex]h(3)=-9+18+7\\h(3)=16[/tex]
The ball will be 16 units high after travelling 3 units horizontally. This is the maximum height the ball will reach before falling.
