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

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 .

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 .

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.

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

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 a product of factors equals 0, at least one of the factors must also equal 0.

In the equation \(0 = -12x(x - 20)\), Leon can set each factor equal to 0:

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

Now, let's solve these equations:

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

Thus, the two values of \(x\) are 0 and 20. This means the ball hits the ground at a horizontal distance of 0 (when it is kicked) and at 20 (when it lands).

Therefore, to answer the original question, Leon can use the Zero Product Property to solve the two equations: \(-12x = 0\) and \(x - 20 = 0\).

The correct response is:

Solve the two equations: −12x=0 and x−20=0.