The height of a kicked football during a field goal attempt can be approximated by h=-0.0114x^2 + 1.732x, where h is the height, in feet, of the football when it is x feet from the kicker. To clear the goalpost the football must be at least 10 feet above the ground. What is the maximum number of yards the kicker can be from the goalpost to that the football clears it? Round to the nearest tenth of a yard.
I plugged the equation given into my calculator and I get a reasonable parabola that starts from the origin. Everything looks fine. The answer in the back of the book is 48.6. However, when I trace the line the numbers I get as I approach/pass 10 once and again are about 6 and about 145. If I look at x when it's around 48.6 (the answer in the book) the height is approx 57.5 and still climbing to the apex.
What am I doing wrong?