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.[tex]y=0.017x^{2} +0.98x+0.33[/tex]
How far away did the ball land? Estimate to 2 places after the decimal.

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goddessboi goddessboi · Answer 1 · 2022-01-21T21:28:38+01:00

Answer:

57.98 yards

Step-by-step explanation:

When the ball is on the ground, the height is [tex]y=0[/tex], therefore:

[tex]y=-0.017x^2+0.98x+0.33[/tex]

[tex]0=-0.017x^2+0.98x+0.33[/tex]

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} [/tex]

[tex]x=\frac{-0.98\pm\sqrt{0.98^2-4(-0.017)(0.33)}}{2(-0.017)} [/tex]

[tex]x_1=57.98184919[/tex]

[tex]x_2=-0.3347903693[/tex]

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