Finding the x-intercepts of a quadratic function: Step-by-step guide with examples

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

To find the x-intercepts of the quadratic function f(x) = (x – 4)(x + 2), you need to set the function equal to zero and solve for x

To find the x-intercepts of the quadratic function f(x) = (x – 4)(x + 2), you need to set the function equal to zero and solve for x.

Setting f(x) equal to zero:

0 = (x – 4)(x + 2)

Now, you can use the zero-product property. According to this property, if a product of factors is equal to zero, then at least one of the factors must be zero.

Therefore, we can set each factor equal to zero and solve for x separately.

Setting x – 4 = 0:

x – 4 = 0
x = 4

Setting x + 2 = 0:

x + 2 = 0
x = -2

So, the x-intercepts of the quadratic function f(x) = (x – 4)(x + 2) are x = 4 and x = -2.

In terms of the given options, the x-intercepts are represented by the points (-4, 0) and (4, -2).

Therefore, the correct answer is (-4, 0).

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