Which point is an x-intercept of the quadratic function f(x) = (x - 4)(x + 2)?
(-4, 0), (-2, 0), (0, 2), (4, -2)

Solution:

The x-intercept for any curve is the value of x coordinate of the point where the graph cuts x-axis, or we can say that x-intercept is the value of the x coordinate of a point where the value of y coordinate equal to zero.

Given, f(x) = (x - 4)(x + 2)

Now, change the function into an equation,

f(x) = y

y = (x - 4)(x + 2)

When y = 0,

0 = (x - 4)(x + 2)

⇒ x - 4 = 0

⇒ x = 0 + 4

⇒ x = 4

⇒ x + 2 = 0

⇒ x = 0 - 2

⇒ x = -2

So, the value of x is 4 and -2.

Therefore, (-2, 0) is the x-intercept.

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Which point is an x-intercept of the quadratic function f(x) = (x - 4)(x + 2)?

Summary:

The point (-2, 0) is an x-intercept of the quadratic function f(x) = (x - 4)(x + 2).