Determine the number of x-intercepts that appear on a graph of each function. f(x)= (x-6)^2(x+2)^2

Question

Determine the number of x-intercepts that appear on a graph of each function. f(x)= (x-6)^2(x+2)^2

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Caroline 1 week 2021-09-10T12:52:19+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T12:53:32+00:00

    Answer:

    the awnser is 2

    Step-by-step explanation:

    0
    2021-09-10T12:53:37+00:00

    Answer:

    Two x-intercepts x = -2 and x = 6

    Step-by-step explanation:

    f(x)=(x-6)^2(x+2)^2\to y=(x-6)^2(x+2)^2

    x-intercepts are for y = 0.

    Put y = 0 to the equation:

    (x-6)^2(x+2)^2=0\iff(x-6)^2=0\ \vee\ (x+2)^2=0\\\\(x-6)^2=0\iff x-6=0\qquad\text{add 6 to both sides}\\\\x=6\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\x=-2

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