Find the vertex of the parabola whose equation is y = x 2 + 8x + 12. (-4, 12) (-4, -4) (0, -6)

Question

Find the vertex of the parabola whose equation is y = x 2 + 8x + 12.
(-4, 12)
(-4, -4)
(0, -6)

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Gabriella 3 weeks 2021-10-10T18:52:32+00:00 1 Answer 0

Answers ( )

    0
    2021-10-10T18:53:42+00:00

    Answer:

    (-4, -4)

    Step-by-step explanation:

    You have to put this in vertex form by completing the square in order to determine the vertex.  Begin by setting the quadratic equal to 0 then moving the 12 over by subtraction:

    x^2+8x=-12

    The rules are to take half the linear term, square it, and add it to both sides.  Our linear term is 8.  Half of 8 is 4, and 4 squared is 16.  So we add 16 to both sides:

    (x^2+8x+16)=-12+16

    During this process we have created a perfect square biomial on the left. We will state that, along with simplifying on the right:

    (x+4)^2=4

    Now we will move the 4 back over and set it back to equal y:

    (x+4)^2-4=y

    And from this you can see that the coordinates of the vertex are (-4, -4)

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