The height y in feet of a ball thrown by a child is y 112

The height y (in feet) of a ball thrown by a child is y = - 1/12 x^2 + 2x + 5 where x is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child\'s hand? (b) What is the maximum height of the ball? (c) How far from the child does the ball strike the ground?

Solution

y = -x^2/12 + 2x +5 where x is the horizontal distance

a) when x =0 ; y = 5 feet is the height of ball

b) maximum height : vertex x = -b/2a = - (2/2*(-1/12) ) = 12 feet horizontal distance

ymax = -(12)^2/12 +2*12 +5 = 17 feet

c) ball strikes the ground when y =0

-x^2/12 + 2x +5 =0

solve for x : x = - 2.283 , 26.283

Neglect -ve .

So, x = 26.28 feet balls on the ground