Question

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) 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 . 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. Plug in 0 for all the x terms in the function. Solve the two equations: −12x=0 and x−20=0.

Answer 1

To find the horizontal distance the soccer ball has traveled when its height is 0, Leon can indeed use the Zero Product Property. The equation he has is:

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

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

So, Leon can set each factor equal to zero:

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

Now he can solve each equation:

1. From \(-12x = 0\): \[ x = 0 \]

2. From \(x - 20 = 0\): \[ x = 20 \]

Therefore, the horizontal distances when the height of the soccer ball equals 0 are \(x = 0\) and \(x = 20\). This means the ball hits the ground at these two points: when it was kicked (at 0 horizontal distance) and when it lands (at 20 horizontal distance).

So the correct response to use the Zero Product Property is:

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