The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football?

The parabola opens downward because the coefficient of x² is −0.04, so its vertex gives the maximum height. The vertex occurs at x = −1.56 ÷ (2 × −0.04) = 19.5 yards. Substituting gives y = −0.04(19.5)² + 1.56(19.5) = 15.21 yards, so the approximate maximum height is 15.21 yd.

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