Question 54866
Transform the general equation y=ax^2+bx+c to vertex form {{{highlight(y=a(x-h)^2+k)}}}, where the vertex=(h,k).
{{{y=a(x^2+bx/a)+c}}}
{{{y=a(x^2+bx/a+(b/2a)^2)-a(b/2a)^2+c}}}
{{{y=a(x+b/2a)^2-b^2/4a+c}}}
{{{y=a(x+b/2a)^2-b^2/4a+4a/c}}}
{{{y=a(x+b/2a)^2+(-b^2+4ac)/4a}}}
:
Check:
{{{y=a(x^2+2bx/2a+b^2/4a^2)+(-b^2+4ac)/4a}}}
{{{y=ax^2+2abx/2a+ab^2/4a^2-b^2/4a+4ac/4a}}}
{{{y=ax^2+bx+b^2/4a-b^2/4a+c}}}
{{{y=ax^2+bx+c}}}
:
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/2a}}} (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=(-b^2+4ac)/4a)}}}Good Luck!!!
Happy Calculating!!!