How do you find the standard form of the equation of the parabola with a vertex of (-1,4) and x intercepts of (-3,0) and (1,0)?

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Answer 1 · 2016-11-28T05:19:19

Please see the explanation.

If the x intercepts are $(-3,0) and (1,0)$ , then $(x + 3)$ and $(x - 1)$ are factors:

$y = k(x + 3)(x - 1)$

To find the value of k, substitute -1 for x and 4 for y:

$4 = k(-1 + 3)(-1 - 1)$

$4 = k(2)(-2)$

$k = -1$

$y = -1(x + 3)(x - 1)$

Use the F.O.I.L. method to multiply the binomials:

$y = -1(x^2 -x + 3x - 3)$

$y = -1(x^2 + 2x - 3)$

Distribute the -1:

$y = -x^2 - 2x + 3$

This is standard form.