Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)? a: (0,6) b: (0,–6) c: (6,0) d: (–6,0)

D is the only x-intercept out of the options listed below.

In order to find an x-intercept, you need a value that will cause the y-value to equal 0, since this is where x-intercepts exist.

Automatically, A and B do not work since the y-values in the ordered pairs do not equal 0. By definition they are not x-intercepts. Next we can try the x-values in the equation to see which gives us a 0 y-value.

C

f(x) = (x + 6)(x - 3)

f(6) = (6 + 6)(6 - 3)

f(6) = (12)(3)

f(6) = 36

Since this does not equal 0, it is not an x-intercept.

D

f(x) = (x + 6)(x - 3)

f(-6) = (-6 + 6)(-6 - 3)

f(-6) = (0)(-9)

f(-6) = 0

This shows us that D yields a 0 value for y and is thus a x-intercept.

figure c

step-by-step explanation:

hope this .