SOLUTION: write the equation of the parabola with the same shape as f(x)=-2x^2 but with the vertex (-3,2).

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Question 150468: write the equation of the parabola with the same shape as f(x)=-2x^2 but with the vertex (-3,2).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Go back to the general formula for a parabola which is
y+=+ax%5E2+%2B+bx+%2B+c
The formula for the x-coordinate of the vertex is %28-b%29+%2F+%282a%29
With the parabola y+=+-2x%5E2,
a+=+-2
b+=+0
c+=+0
So, x+=+0+%2F+2%2A%28-2%29+=+0
and
y+=+-2%2A%280%29%5E2
y+=+0
So, the vertex of this parabola is (0,0). You are asked to keep the
shape the same, but move the vertex to (-3,2)
I can say %28-b%29+%2F+%282a%29+=+-3
I don't want a to change, because that would change the shape, so
a+=+-2
%28-b%29+%2F+2%2A%28-2%29+=+-3
-b+=+12
b+=+-12
So far, I have y+=+-2x%5E2+-+12x+%2B+c
I can use (-3,2) to find c
2+=+-2%2A%28-3%29%5E2+-+12%2A%28-3%29+%2B+c
2+=+-18+%2B+36+%2B+c
c+=+2+%2B+18+-+36
c+=+-16
y+=+-2x%5E2+-+12x+-+16 answer
I'll plot both these equations
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%5E2%2C+-2x%5E2+-+12x+-+16%29+
Each vertex looks OK