The part of a football kicked by a field goal kicker can be modeled by the equation y=-0.03x2 + 1.53x, where is x the horizontal distance in yards and y the corresponding height in yards . what is the footbal's maximun height? round to the nearest tenth

The max of a quadratic is given by x = -b / (2a). Notice x instead of y.
For the given equation, a=.03 and b=1.53 (and c=0).
x = - 1.53 / (2*(-.03)) = 25.5.
Now plug it in to the equation to get y (the height)
y = -.03(25.5)^2+1.53(25.5) = 19.508

The max height is 19.508 yards.