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.

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.

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
.

Answer 1

To find the horizontal distance the ball has traveled when the height equals 0 using the Zero Product Property, Leon can rewrite the equation as:

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

According to the Zero Product Property, if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. In this case, the two factors are \(-12x\) and \(x - 20\).

Setting each factor equal to zero gives:

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

Now, solving these equations:

1. For \(-12x = 0\):

   • Divide both sides by \(-12\):
   • This simplifies to \(x = 0\).

2. For \(x - 20 = 0\):

   • Add \(20\) to both sides:
   • This simplifies to \(x = 20\).

Thus, the possible values of \(x\) when the height \(h(x)\) equals 0 are \(x = 0\) and \(x = 20\).

The horizontal distance the ball has traveled when it hits the ground (height = 0) is:

• At \(x = 0\) (when the ball was initially kicked) and
• At \(x = 20\) (when it hits the ground).

The response that correctly describes how to use the Zero Product Property here is:

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