Respuesta :
The maximum height of the football is 15.21 yards.
Maximum height of parabola
The maximum height is the vertex of the parabola, when the parabola faces down.
Given
The path of a football kicked by a field goal kicker can be modeled by the equation y = -0.04x^2 + 1.56x.
Where x is the horizontal distance in yards and y is the corresponding height in yards.
The x- coordinate of the vertex is given by;
[tex]\rm x=\dfrac{-b}{2a}[/tex]
The value of b is 1.56, and a is -0.04.
Substitute all the values in the equation
[tex]\rm x=\dfrac{-b}{2a}\\\\x=\dfrac{-1.56}{-0.08}\\\\x=19.5[/tex]
Substitute the value of x in the given equation
[tex]\rm y = -0.04x^2 + 1.56x\\\\ y = -0.04(19.5)^2+1.56(19.5)\\\\y = - 15.21 + 30.42 \\\\ y=15.21 \ yd[/tex]
Hence, the maximum height of the football is 15.21 yards.
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