The path of a soccer ball can be modeled by the equation h(x)=−1/2x(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=−1/2x(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. Solve the two equations: −1/2x=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 . Plug in 0 for all the x terms in the function. Plug in 0 for all the x terms in the function. Cancel out the x and then multiply −1/2 and −20.

Question

The path of a soccer ball can be modeled by the equation h(x)=−1/2x(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=−1/2x(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. Solve the two equations: −1/2x=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 . Plug in 0 for all the x terms in the function. Plug in 0 for all the x terms in the function. Cancel out the x and then multiply −1/2 and −20.

Answer 1

To find the horizontal distance the ball has traveled when the height is equal to 0, Leon can use the Zero Product Property. He can set the equation -1/2x(x-20) = 0.

By setting this equation equal to 0, he can solve for x.

Therefore, the correct answer is:
Solve the two equations: -1/2x = 0 and x-20 = 0

Answer 2

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. The Zero Product Property states that if a product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

In this case, Leon needs to solve the equation 0 = -1/2x(x - 20) by setting each factor equal to zero.

Setting -1/2x = 0, we can solve for x:

-1/2x = 0
Divide both sides by -1/2 to isolate x:
x = 0

Setting (x - 20) = 0, we can solve for x:

x - 20 = 0
Add 20 to both sides to isolate x:
x = 20

Now that we have two possible values for x (x=0 and x=20), we can plug them back into the original equation to find the corresponding heights:

For x = 0:
h(0) = -1/2(0)(0-20)
h(0) = 0

For x = 20:
h(20) = -1/2(20)(20-20)
h(20) = -1/2(20)(0)
h(20) = 0

Both values of x give us a height of 0, meaning the ball hits the ground when the height is 0. Therefore, the ball hits the ground at x = 0 and x = 20.

So, Leon can use the Zero Product Property to find that the ball has traveled 0 units when it hits the ground.

Answer 3

In order 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. The Zero Product Property states that if a product of two factors equals zero, then at least one of the factors must equal zero.

In this case, Leon has the equation 0 = -1/2x(x-20). By setting the equation equal to zero, he can find the values of x that would make the equation true.

So, Leon needs to solve the equation -1/2x(x-20) = 0.

To do this, he can set each factor in the equation equal to zero and solve for x.

First, he sets the first factor, -1/2x, equal to zero:

-1/2x = 0

Then, he can solve this equation for x by dividing both sides by -1/2:

x = 0

Next, he sets the second factor, (x-20), equal to zero:

x-20 = 0

Then, he can solve this equation for x by adding 20 to both sides:

x = 20

So, Leon has found two possible values of x: x = 0 and x = 20.

To determine the horizontal distance the ball has traveled when the height is 0, he can substitute these values back into the original equation h(x) = -1/2x(x-20) and plug in 0 for all the x terms:

For x = 0:

h(0) = -1/2(0)(0-20)
h(0) = -1/2(0)(-20)
h(0) = 0

For x = 20:

h(20) = -1/2(20)(20-20)
h(20) = -1/2(20)(0)
h(20) = 0

Since the height is 0 for both x = 0 and x = 20, this means the ball hits the ground at these two distances.

Therefore, Leon can use the Zero Product Property to find that the ball has traveled a horizontal distance of 0 and 20 units when its height equals 0.