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

Question

, 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)
. 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

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

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

He cannot use the Zero Product Property because the height will never be 0.
He cannot use the Zero Product Property because the height will never be 0.

Cancel out the x and then multiply −12
and −20
.

Answer 1

To find the horizontal distance the ball has traveled when the height of the soccer ball equals 0, Leon can use the Zero Product Property. This property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

Given the equation:

\[ 0 = -12x(x - 20) \]

Leon can set each factor equal to zero:

1. \(-12x = 0\)
2. \(x - 20 = 0\)

Now, solving these equations gives:

1. From \(-12x = 0\), we find \(x = 0\).
2. From \(x - 20 = 0\), we find \(x = 20\).

So, the two values of \(x\) where the height \(h(x)\) is zero are \(x = 0\) and \(x = 20\). This tells us that the ball is at ground level when it starts (at \(x=0\)) and when it has traveled 20 units horizontally.

Therefore, Leon’s correct course of action is:

Solve the two equations: \(-12x = 0\) and \(x - 20 = 0\).