SOLUTION: Write the equation of the parabola in vertex form, with an axis of symmetry of x=4 passing through (1,-13) and (-1,-45)

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Question 1020397: Write the equation of the parabola in vertex form, with an axis of symmetry of x=4 passing through (1,-13) and (-1,-45)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Thinking about that sketch either in the head or on paper, leading coefficient a%3C0.

y=a%28x-4%29%5E2%2Bk standard form using known symmetry axis.


--
a%28x-4%29%5E2%2Bk=y

a%281-4%29%5E2%2Bk=-13
9a%2Bk=-13
-
a%28-1-4%29%5E2%2Bk=-45
25a%2Bk=-45
-
Find a and k in this system, preferably beginning with Elimination Method...
system%289a%2Bk=-13%2C25a%2Bk=-45%29.

9a-25a=-13-%28-45%29
-16a=45-13
-16a=32
8a=-16
highlight%28a=-2%29
Use this to find k, either equation. Either point

a%28x-4%29%5E2%2Bk=y
k=y-a%28x-4%29%5E2
k=-13-%28-2%29%281-4%29%5E2
k=-13%2B2%28-3%29%5E2
k=-13%2B2%2A9
k=18-13
highlight%28k=5%29

Put everything altogether:
highlight%28highlight%28highlight_green%28y=-2%28x-4%29%5E2%2B5%29%29%29