Question

Write y=2x^2+12x+14 in vertex form.

Answer 1

Use completing the square

Answer 2

\[y=2x^2+12x+14)\\y=2(x^2+6x)+7(2)\\ \\ \ \text{ Complete the square:}\\ y=2( x^2 +6x+(\frac{ 6 }{ 2 })^2) +7(2)-(2)(\frac{ 6}{2})^2 \\y= 2(x^2 +6x+(\frac{ 6 }{ 2 })^2) +14-18 \\y=2(x^2+6x+ 9 ) - 4 \\y= 2(x +3 )^2 - 4\\ \text{The vertex for a }\\ \text{Quadratic Equation in the form :}\\y= (x -h )^2 +k \\ \text{is} \ (h,k)\\\text{ So, here, the Vertex is :}\\( -3 , -4) \]