Question

What is the vertex for the graph of y = 2x2 + 12x + 10?

Answer 1

\[\large y=2x^2+12x+10\]


\[\large y=2(x^2+6x+5)\]


\[\large y=2(x^2+6x+9-9+5)\]


\[\large y=2((x^2+6x+9)-9+5)\]


\[\large y=2((x+3)^2-9+5)\]


\[\large y=2((x+3)^2-4)\]


\[\large y=2(x+3)^2-8\]


\[\large y=2(x-(-3))^2-8\]


Equation is now in the form \[y=a(x-h)^2+k\] where the vertex is (h,k)


Since h=-3 and k=-8, this means that the vertex is (-3,-8)