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 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. 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.

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 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. 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

The correct answer is: Solve the two equations: −12x=0 and x−20=0.

Answer 2

To use the Zero Product Property to find the horizontal distance the ball has traveled when the height is 0, Leon needs to set the equation equal to 0: 0 = -12x(x - 20).

Then, he can either plug in 0 for all the x terms in the function which becomes: 0 = -12(0)(0 - 20).

Or he can solve the two equations separately: -12x = 0 and x - 20 = 0.

To solve the equation -12x = 0, he can cancel out the x by dividing both sides by -12, which gives x = 0.

To solve the equation x - 20 = 0, he can add 20 to both sides to isolate x, which gives x = 20.

So, by using the Zero Product Property and solving the equations, Leon can determine that the horizontal distance the ball has traveled when the height is 0 is x = 0 and x = 20.

Answer 3

Leon can use the Zero Product Property to find the horizontal distance the ball has traveled when the height of the soccer ball equals 0. The Zero Product Property states that if AB = 0, then either A = 0 or B = 0.

In this case, he can set the equation 0 = -12x(x - 20) equal to 0 and use the Zero Product Property to find the values of x for which the height of the ball equals 0.

To do this, he can set each factor of the equation equal to 0 and solve for x:

1) -12x = 0
By dividing both sides of the equation by -12, we get x = 0.

2) (x - 20) = 0
By adding 20 to both sides of the equation, we get x = 20.

So, the values of x for which the height of the soccer ball equals 0 are x = 0 and x = 20. Therefore, the soccer ball hits the ground at two different horizontal distances: 0 units and 20 units.