Question

Suppose a soccer goalie punted the ball in such a way as to kick the ball as far as possible down the field. The height of the ball above the field can be approximated by the function below where y represents the height of the ball (in yards) and x represents the horizontal distance (in yards) down the field from where the goalie kicked the ball.$y=0.017x^{2} +0.98x+0.33$
How far away did the ball land? Estimate to 2 places after the decimal.

Answer 1

Answer:

57.98 yards

Step-by-step explanation:

When the ball is on the ground, the height is $y=0$, therefore:

$y=-0.017x^2+0.98x+0.33$

$0=-0.017x^2+0.98x+0.33$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-0.98\pm\sqrt{0.98^2-4(-0.017)(0.33)}}{2(-0.017)}$

$x_1=57.98184919$

$x_2=-0.3347903693$

Since distance cannot be negative, the ball landed 57.98 yards down the field from where the goalie kicked the ball.