Question
Kim throws her basketball up from the ground toward the basketball hoop from a distance of 20 feet away from the hoop. The ball follows a parabolic path and returns back to the gym floor 5 feet from the hoop. Write one possible equation to represent the path of the basketball. Explain your answer. Answer to this question.
Answers
Poorly worded question.
Assuming her position is at the origin, and assuming by "path of ball" you mean the height of the ball, and assuming the net is at (20,10), and assuming the ball lands 5 ft beyond the net, we could have ....
height = ax(x-25)
subbing in (20,10)
10 = a(20)(-5)
10 = -100a
a = -1/10
height = (-1/10)(x)(x-25)
or (-1/10)x^2 + (5/2)x
check:
the 3 points (0,0) , (20,10) and (25,0) should satisfy the equation
when x = 0 , height = 0 , check!
when x = 20, height = (-1/10)(400) + (5/2)(20)
= -40 + 50 = 10
when x = 25 , height = 0
my equation is correct
Assuming her position is at the origin, and assuming by "path of ball" you mean the height of the ball, and assuming the net is at (20,10), and assuming the ball lands 5 ft beyond the net, we could have ....
height = ax(x-25)
subbing in (20,10)
10 = a(20)(-5)
10 = -100a
a = -1/10
height = (-1/10)(x)(x-25)
or (-1/10)x^2 + (5/2)x
check:
the 3 points (0,0) , (20,10) and (25,0) should satisfy the equation
when x = 0 , height = 0 , check!
when x = 20, height = (-1/10)(400) + (5/2)(20)
= -40 + 50 = 10
when x = 25 , height = 0
my equation is correct