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)%0D%0AResponses%0D%0A%0D%0AHe cannot use the Zero Product Property because the height will never be 0.%0D%0AHe cannot use the Zero Product Property because the height will never be 0.%0D%0A%0D%0APlug in 0 for all the x terms in the function.%0D%0APlug in 0 for all the x terms in the function.%0D%0A%0D%0ACancel out the x and then multiply −12 and −20.%0D%0ACancel out the x and then multiply negative Start Fraction 1 over 2 End Fraction and negative 20 .%0D%0A%0D%0ASolve the two equations: −12x=0 and x−20=0.

Answer 1

To find the horizontal distance the soccer ball has traveled when it hits the ground, Leon can use the Zero Product Property effectively on the equation he set up:

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

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must equal zero. This means that Leon can set each factor in his equation equal to zero and solve for \( x \).

The two factors here are:

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

Now, let's solve these equations:

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

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

Thus, the solutions are \( x = 0 \) and \( x = 20 \). This means that the ball is at a height of 0 (ground level) when the horizontal distance \( x \) is 0 (the starting point) and when it is 20 units away.

Therefore, the correct response to your question is:

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