What are the x-intercepts of y = (x − 2)(x + 5)?
(0, 2) and (0, −5)
(0, −2) and (0, 5)
(−2, 0) and (5, 0)
(2, 0) and (−5, 0)

Step-by-step explanation:

x-intercepts exist when y = 0.  Set the quadratic equal to 0 and solve each expression for x:

0 = (x - 2)(x + 5)

By the Zero Product Property, either x - 2 = 0 or x + 5 = 0 (because when you multiply 0 by anything, you get a 0. Which means that one of these expressions has to equal 0.)

x - 2 = 0 so

x = 2

x + 5 = 0 so

x = -5

Again, the x-intercept exists when y = 0, so the number for y in the coordinates will be 0's. (2, 0) and (-5, 0) are your coordinates.

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