Question

Equation of a parabola y = (x + 5)(x - 7)

What are the coordinates of the x-axis intercepts?

A. (5, 0) and (7, 0)

B. (-5, 0) and (7, 0)

C. (5, 0) and (-7, 0)

D. (-5, 0) and (-7, 0)​

Answer 1

B. (-5, 0) and (7, 0)

Explanation:

Here are the steps to find the x-axis intercepts of the parabola with the equation y = (x + 5)(x - 7):

Set y equal to zero: y = 0.

Substitute y with 0 in the equation: 0 = (x + 5)(x - 7).

Set each factor equal to zero: (x + 5) = 0 and (x - 7) = 0.

Solve the first equation: x + 5 = 0. Subtract 5 from both sides: x = -5.

Solve the second equation: x - 7 = 0. Add 7 to both sides: x = 7.

Therefore, the x-axis intercepts are x = -5 and x = 7, which correspond to the points (-5, 0) and (7, 0) on the coordinate plane.