The path of a soccer ball can be modeled by the equation h(x)=−12x(x−20)

Question

ℎ
(
𝑥
)
=
−
1
2
𝑥
(
𝑥
−
20
)
, where h(x) is the height of the ball, and x is the horizontal distance the ball has traveled. To determine how far the ball has traveled when it hits the ground, Leon set the height equal to 0 and obtained the equation: 0=−12x(x−20)
0
=
−
1
2
𝑥
(
𝑥
−
20
)
. How can he use the Zero Product Property to find the horizontal distance the ball has traveled when the height of the soccer ball equals 0?(1 point)
Responses

Solve the two equations: −12x=0
−
1
2
𝑥
=
0
and x−20=0
𝑥
−
20
=
0
.
Solve the two equations: negative Start Fraction 1 over 2 End Fraction x equals 0 and x minus 20 equals 0 .

Cancel out the x and then multiply −12
−
1
2
and −20
−
20
.
Cancel out the x and then multiply negative Start Fraction 1 over 2 End Fraction and negative 20 .

Plug in 0 for all the x terms in the function.
Plug in 0 for all the

Answer 1

To use the Zero Product Property, Leon should solve the equation by setting each factor in the equation \( 0 = -\frac{1}{2}x(x - 20) \) equal to zero. This leads to two equations:

1. \(-\frac{1}{2}x = 0\)
2. \(x - 20 = 0\)

Solving these:

1. \(-\frac{1}{2}x = 0\) gives \(x = 0\).
2. \(x - 20 = 0\) gives \(x = 20\).

Therefore, the ball hits the ground (height equals 0) when \(x = 0\) (the starting point) and \(x = 20\) (the point where it lands).

So the best response is: Solve the two equations: \(-\frac{1}{2}x = 0\) and \(x - 20 = 0\).