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6 May, 23:03

Find the x-intercept of the parabola of with vertex (1,20) and the y-intercept (0,16). write your answer in this form: (x1, y1), (x2, y2)

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  1. 6 May, 23:09
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    I assume that the parabola in this particular problem is one whose axis of symmetry is parallel to the y axis. The formula we're going to use in this case is (x-h) 2=4p (y-k). We know variables h and k from the vertex (1,20) but p is not given. However, we can solve for p by substituting values x and y in the formula with the y-intercept:

    (0-1) ^2=4p (16-20)

    Solving for p, p=-1/16.

    Going back to the formula, we can finally solve for the x-intercepts. Simply fill in variables p, h and k then set y to zero:

    (x-1) ^2=4 (-1/16) (0-20)

    (x-1) ^2=5

    x-1 = (+-) sqrt (5)

    x = (+-) sqrt (5) + 1

    Here, we have two values of x

    x=sqrt (5) + 1 and

    x=-sqrt (5) + 1

    thus, the answers are: (sqrt (5) + 1,0) and (-sqrt (5) + 1,0).
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