Use the table to answer the question. The table shows:
(x + 3)(x + 4) = 0
x - 3 = 0 x + 4 = 0
x = 3 x = -4
While the Zero Product Property to find the values of x that make the quadratic equals 0, Oliver completed the work provided in the table. Is Oliver's work accurate?
A. Yes, the work is accurate.
B. No, x - 3 = 0 in the second row should be x + 3 = 0.
C. No, he should have a third column where he should set x = 0.
D. No, x + 4 = 0 in the second row should be x - 4 =0.
B. No, x - 3 = 0 in the second row should be x + 3 = 0.
D. At least one of the factors, ( 2x - 3 ) or ( x + 2 ), must equal 0 for the entire function to equal 0.
B. Solve the two equations: -1/2x = 0 and x - 20 = 0.
Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x - 3) ( x + 2 ) = 0?
A. No values of x will make the function equal 0.
B. Both factors, ( 2x - 3 ) or ( x + 2 ), must equal 0 for the entire function to equal 0.
C. Neither of the factors, ( 2x - 3 ) or ( x + 2 ), must equal 0 for the entire function to equal 0.
D. At least one of the factors, ( 2x - 3 ) or ( x + 2 ), must equal 0 for the entire function to equal 0.
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?
A. Plus in 0 for all the x terms in the function.
B. Solve the two equation: -1/2x = 0 and x - 20 = 0.
C. he cannot use the Zero Product Property because the height will never be 0.
D. Cancel out the x and then multiply -1/2 and -20.
Solve the factored quadratic equation 0 = -1/3x ( x - 6).
A. The solution set is x = { -6, 3 }
B. The solution set is x = { 1/3, 6 }
C. The solution set is x = { 0, 6 }
D. The solution set is x = { 0, -6 }
A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given by the function h (x) = -1/25x ( x - 45 ), where h (x) is the height of the golf ball and x is the horizontal distance it has traveled. Solve the equation to determine how far the ball will have traveled when it hits the ground. How far will the ball need to roll to make it to the hole?
0 = -1/25x ( x - 45 )
A. The ball will hit the ground after is has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.
B. The ball will hit the ground after is has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.
C. The ball will hit the ground after is has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.
D. The ball will hit the ground after is has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.
The Zero Product Property states that if a product of factors is equal to zero, then at least one of the factors must be zero. In this case, we have the quadratic equation (x + 3)(x + 4) = 0.
To find the values of x that make the quadratic equal to zero, we set each factor equal to zero and solve for x. Oliver correctly set up the two equations x - 3 = 0 and x + 4 = 0, which represent each factor of the quadratic equation.
Now, let's analyze each option to determine if Oliver's work is accurate:
A. Yes, the work is accurate. - This option states that Oliver's work is accurate. We need to check if this is true.
B. No, x - 3 = 0 in the second row should be x + 3 = 0. - This option suggests that Oliver made an error in the second row. However, Oliver correctly wrote x - 3 = 0, which is equivalent to x + 3 = 0. This statement is wrong.
C. No, he should have a third column where he should set x = 0. - This option suggests that Oliver made a mistake by not including a third column to set x equal to 0. However, solving for x = 0 is not necessary in this equation since it does not yield any additional solutions. Therefore, this statement is incorrect.
D. No, x + 4 = 0 in the second row should be x - 4 =0. - This option suggests that Oliver made a mistake in the second row. However, Oliver correctly wrote x + 4 = 0, which is equivalent to x - 4 = 0. This statement is also incorrect.
After analyzing each option, we can conclude that the correct answer is A. Yes, the work is accurate. Oliver's work correctly represents the Zero Product Property, setting each factor equal to zero to find the values of x that make the quadratic equation equal to zero.