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

Question

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

y= -1/12x^2 + 2x + 3

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? (Hint: Find y when x=0)

your answer is y=

(b) What is the maximum height of the ball? 

(c) How far from the child does the ball strike the ground? 

Answer 1

y = -x²/12+2x+3

a) y(0) = 3

b) This is a parabola, ax²+bx+c. The value of x at the vertex of a parabola is:

x = -b/(2a) = -2/(2(-1/12)) = 12

y(12) = -144/12+24+3 = 15

c) This is when y = 0 = -x²/12+2x+3

x = (-2±√(4+4(1/12)(3))/(-2/12) = 12 ± 6√5

Choose the positive value, x = 12+6√5≈25.416