The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.03x2 + 1.53x, where x is the horizontal distance in yards and y is the corresponding height in yards. what is the football’s maximum height? round to the nearest tenth. yds. how far is the football kicked? yds.

Maximum height achieved by football = 25.5 yards.

Distance traveled by football  51 yards.

Step-by-step explanation:

Path of a football kicked by a field goal kicker can be modeled by the equation y = -0.03x² + 1.53x.

Where x represents horizontal distance and y represents height of the football.

For maximum, height we will find the ( derivative ) of the equation and equate it to zero.

= (-0.03x² + 1.53x )

= -0.03 × 2x + 1.53

By putting = 0

-0.06x + 1.53 = 0

0.06x = 1.53

x = = 25.5 yards

Therefore, maximum height achieved by the ball is  25.5 yards.

Now for horizontal distance covered by ball y should be 0

-0.03x² + 1.53x = 0

x ( 1.53 - 0.03x ) = 0

0.03x = 1.53

x = = 51 yards.

Football was kicked 51 yards.

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