The Zero Product Property states that if a product of two factors is zero, then at least one of the factors must be zero. For the equation given:
0 = -12x(x - 20)
The two factors are -12x and (x - 20). According to the Zero Product Property, we set each factor equal to zero and solve for x:
For -12x:
-12x = 0
Divide both sides by -12 to isolate x:
x = 0
For (x - 20):
x - 20 = 0
Add 20 to both sides to solve for x:
x = 20
Therefore, by using the Zero Product Property, Leon can conclude that the horizontal distances at which the height of the soccer ball equals 0 are 0 and 20 units. This means the ball starts at ground level (when x = 0), reaches its peak, and then hits the ground again after traveling a horizontal distance of 20 units (when x = 20).
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
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 .
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.
Cancel out the x and then multiply −12 and −20.
3 answers
so it is c
My apologies for any confusion, but the correct application of the Zero Product Property in this case is option (b):
"Solve the two equations: −12x = 0 and x−20 = 0."
Leon needs to solve these two separate equations to find the values of x when the height of the ball, h(x), equals zero. By doing this, he will find the horizontal distances where the ball is on the ground:
For −12x = 0, solving for x gives x = 0.
For x - 20 = 0, solving for x gives x = 20.
The horizontal distances the ball has traveled when the height is zero are at x = 0 (where the ball is kicked) and at x = 20 (where the ball lands).
"Solve the two equations: −12x = 0 and x−20 = 0."
Leon needs to solve these two separate equations to find the values of x when the height of the ball, h(x), equals zero. By doing this, he will find the horizontal distances where the ball is on the ground:
For −12x = 0, solving for x gives x = 0.
For x - 20 = 0, solving for x gives x = 20.
The horizontal distances the ball has traveled when the height is zero are at x = 0 (where the ball is kicked) and at x = 20 (where the ball lands).