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

Question

Responses

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

Answer 1

To find the horizontal distance the ball has traveled when the height of the soccer ball equals 0 using the Zero Product Property, Leon can set each factor of the equation equal to zero. From the equation \( 0 = -12x(x - 20) \), we can use the Zero Product Property which states that if a product of factors equals zero, at least one of the factors must be zero.

The factors in the equation are \(-12x\) and \(x - 20\). Setting each factor equal to zero gives:

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

Now, solving each equation:

1. From \(-12x = 0\), we divide both sides by \(-12\), which gives us \(x = 0\).
2. From \(x - 20 = 0\), we add 20 to both sides, which gives us \(x = 20\).

Thus, the two solutions for the horizontal distance when the height is 0 (the point where the ball hits the ground) are \(x = 0\) and \(x = 20\).

Therefore, the correct response is: Solve the two equations: \(-12x=0\) and \(x−20=0\).