Question

3.1 Q15

Answer 1

The maximum height of the shot is represented by the y-coordinate of the vertex, and the horizontal distance when the maximum height occurs is represented by the x-coordinate of the vertex.

Find x-coordinate of the vertex (horizontal distance)
The function above is in standard form of ax² + bx + c = 0
In standard form of ax² + bx + c = 0, we could find the x-coordinate of the vertex by the formula of
$x= -\cfrac{b}{2a}$

Extract the information of a and b from the function f(x) = -0.06x² + 2.7x + 5.9
a = -0.06
b = 2.7

Input the value of a and b to the formula of x-coordinate of the vertex
x = $-\dfrac{b}{2a}$
x = $- \dfrac{2.7}{2 \times (-0.06) \\}$
x = $- \dfrac{2.7}{-0.12}$
x = $\dfrac{2.7}{0.12}$
x = 22.5
The x-coordinate represents the horizontal distance. So the maximum height occurs when the distance is 22.5 feet far from its point of release.

Find y-coordinate of the vertex (the maximum height)
To find the maximum height, input the value of x-coordinate of the vertex to the function.
f(x) = -0.06x² + 2.7x + 5.9
f(22.5) = -0.06(22.5)² + 2.7(22.5) + 5.9
f(22.5) = -0.06(506.25) + 60.75 + 5.9
f(22.5) = -30.375 + 60.75 + 5.9
f(22.5) = 36.275
The maximum height is 36.275 feet