SOLUTION: What is the vertex of the equation y=x^2+12x-4.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: What is the vertex of the equation y=x^2+12x-4.      Log On


   

Question 1009938: What is the vertex of the equation
y=x^2+12x-4.
Found 2 solutions by MathLover1, josgarithmetic:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2%2B12x-4....write it in the vertex form y=a%28x-h%29%5E2%2Bk where h and k are x and y coordinates of the vertex
y=%28x%5E2%2B12x%29-4..........complete square
y=%28x%5E2%2B12x%2Bb%5E2%29-b%5E2-4
y=%28x%5E2%2B12x%2B6%5E2%29-6%5E2-4
y=%28x%2B6%29%5E2-36-4
y=%28x%2B6%29%5E2-40
so, h=-6 and k=-40 and the vertex is at (-6,-40)



Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Use completion of the square to make the transformation from the general form in which the equation is given, to standard form which the question asks.

You can take the generalized model, y=x%5E2%2Bbx%2Bc, complete the square on this, and you can convert into standard form and still show all the same coefficients in the standard form which came from the general form. It begins with adding AND subtracting %28b%2F%282a%29%29%5E2 to the right-side expression. TRY DOING THAT!

Compare these:
system%28y=x%5E2%2B12x-4%2Cy=x%5E2%2Bbx%2Bc%29
you have b=12 and c=-4.