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.