algebra

Hello,
I need help answering a regents question. It is asking me to find the root of an equation. It also includes a graph which I am unable to upload.The equation is y = −x2 − 2x + 8.
-Thank You

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  1. root means what is x when y is zero.

    x^2+2x-8=0
    what multiplies to -8 and adds to 2?

    (x-2)(x+4)=0
    x=2, x=-4 two roots.
    On the graph, the roots are where it crosses the x axis (y=0)

  2. y = −x^2 − 2x + 8 I assume

    Let's look at it by completing the square

    x^2 + 2 x = -y + 8

    x^2 + 2 x + 1 = -y + 9

    (x+1)^2 = -(y-9)

    That is a parabola (upside down, sheds water because of the - in front of y) with an axis of symmetry of x = -1 where (x-1) = 0
    the vertex is on that axis where x-1 = 0 so when y = 9.
    then when y = 0. the "roots":
    (x+1)^2= 9
    so
    x+1 = 3
    or
    x+1 = -3
    so
    (2,0) or (-4,0)

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    posted by Damon
  3. (x+1)^2 = -(y-9)

    That is a parabola (upside down, sheds water because of the - in front of y) with an axis of symmetry of x = -1 where (x+1) = 0
    the vertex is on that axis where x+1 = 0 so when y = 9.
    then when y = 0. the "roots":
    (x+1)^2= 9
    so
    x+1 = 3
    or
    x+1 = -3
    so
    (2,0) or (-4,0)

    1. 👍 0
    2. 👎 0
    posted by Damon

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