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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