Question

A soccer ball is kicked 48 yards and reaches a maximum height of 30 yards. Write the equation of the parabola that describes its path. Leave the vertical stretch factor in exact form

Answer 1

We know that

• The ball is kicked 48 yards.

,

• Its maximum height is 30 yards.

These two numbers defined vertex (48, 30). We use the vertex form

$y=-(x-h)^2+k$

Replacing the vertex, we have

$y=-(x-48)^2+30$

The graph below shows the function.

Therefore, the equation is

$y=-(x-48)^2+30$