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Math Help - Parabola problems

  1. #1
    Junior Member
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    Parabola problems

    Hi,

    I have two problems that I need help with:

    1) Find the vertex of the parabola y=x[squared]+10x+22.

    2) Find the focus of the parabola y[squared]=12x.
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  2. #2
    Junior Member AlvinCY's Avatar
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    Quote Originally Posted by gretchen View Post
    Hi,

    I have two problems that I need help with:

    1) Find the vertex of the parabola y=x[squared]+10x+22.

    2) Find the focus of the parabola y[squared]=12x.

    Hi Gretchen!

    1) The vertex of any parabola in the for y = ax^2 + bx + c occurs at x = -b/(2a), so in this case, it'll happen at x = -10/2 = -5, substituting x = -5 into the equation, y = -3.

    So the vertex is at (-5 , -3)

    2) The focus of the parabola y^2 = 12x. This is a parabola in the for y^2 = 4ax, so it's going to be a parabola facing left or right depending on what a is. Since y^2 = 4 * 3 * x in our situation, our parabola points right, and the focus is at (a,0) = (3,0).
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