SOLUTION: Transform the general equation y=ax^2+bx+c to vertex form.

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Question 54866: Transform the general equation y=ax^2+bx+c to vertex form.
Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
Transform the general equation y=ax^2+bx+c to vertex form highlight%28y=a%28x-h%29%5E2%2Bk%29, where the vertex=(h,k).
y=a%28x%5E2%2Bbx%2Fa%29%2Bc
y=a%28x%5E2%2Bbx%2Fa%2B%28b%2F2a%29%5E2%29-a%28b%2F2a%29%5E2%2Bc
y=a%28x%2Bb%2F2a%29%5E2-b%5E2%2F4a%2Bc
y=a%28x%2Bb%2F2a%29%5E2-b%5E2%2F4a%2B4a%2Fc
y=a%28x%2Bb%2F2a%29%5E2%2B%28-b%5E2%2B4ac%29%2F4a
:
Check:
y=a%28x%5E2%2B2bx%2F2a%2Bb%5E2%2F4a%5E2%29%2B%28-b%5E2%2B4ac%29%2F4a
y=ax%5E2%2B2abx%2F2a%2Bab%5E2%2F4a%5E2-b%5E2%2F4a%2B4ac%2F4a
y=ax%5E2%2Bbx%2Bb%5E2%2F4a-b%5E2%2F4a%2Bc
y=ax%5E2%2Bbx%2Bc
:
Keep in mind that this was done by a human, when there are only letters and variables involved, I can only do but so much to check myself. I checked it against a real quadratic equation in which I could find the vertex. If I'm right the x value of the vertex would be x=-b%2F2a (that actually matches the known formula for the x value of the vertex in an equation written in standard form) and the y value would be y=%28-b%5E2%2B4ac%29%2F4a%29Good Luck!!!
Happy Calculating!!!