U3.L4.HW: Quadratic Functions: Question 28

Question

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

y = -1/14x² + 4x + 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?

_____________ feet

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

____________ feet

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

____________ feet

Answer 1

y= (-1/14)x^2 + 4x + 5

it's 5 feet at time = 0, before it's thrown

y' = -1/7)x +4 = 0

x = 4/1/7 = 28 feet

plug that into the y equation to find max height

y = (-1/14)(28^2) + 4(28) +5

= =-2(28)+4(28) +5

= 2(28) +5

= 56+5

=61 feet = maximum height

(-1/14)x^2 +4x +5 = 0

-x^2 +56 +70 = 0

x^2 -56 -70 = 0

x= 56/2 + (1/2)sqr(56^2 +280)

= 28 +.5sqr3416

= 28 + 29.22

= about 57.22 feet

from the child when it hit the ground