SOLUTION: Find an equation in standard form of the parabola described. Vertex at (-4, -4); passes through (0, 0)

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Question 1162551: Find an equation in standard form of the parabola described.
Vertex at (-4, -4); passes through (0, 0)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are two parabolas that satisfy the given conditions -- one opening up and another opening to the right.

Assuming a parabola that opens up....

The vertex form of the equation of a parabola is

%28y-k%29+=+a%28x-h%29%5E2

where the vertex is (h,k).

So the equation of this parabola is

%28y%2B4%29+=+a%28x%2B4%29%5E2

Use the coordinates of the known point to find the coefficient a:

%280%2B4%29+=+a%280%2B4%29%5E2
4+=+16a
a+=+1%2F4

The equation in vertex form is

%28y%2B4%29+=+%281%2F4%29%28x%2B4%29%5E2

Converting to standard form....

y%2B4+=+%281%2F4%29%28x%5E2%2B8x%2B16%29
y%2B4+=+%281%2F4%29x%5E2%2B2x%2B4
y+=+%281%2F4%29x%5E2%2B2x

A graph, showing the parabola passing through (0,0)....

graph%28400%2C400%2C-6%2C2%2C-6%2C2%2C%281%2F4%29x%5E2%2B2x%29