Question

Convert to vertex form. 
y=2x^2+14x-4

Answer 1

`To \ convert \ the \ standard \ form \ y = ax^2 + bx + c \ of \ a \ function \ into \ vertex \\ \\form \ y = a(x - h)^2 + k \\ \\ Here \ the \ point \ (h, k) \ is \ called \ as \ vertex \\ \\ h=(-b)/(2a) , \ \ \ \ k= c - (b^2)/(4a)`


`y=2x^2+14x-4 \\ \\a=2 ,\ b=14 , \ c=-4 \\ \\ h=(-14)/(2*2)=-(14)/(4)=-3.5 \\ \\k= -4 - (14^2)/(4\cdot 2)=-4-(196)/(8)=-4-24.5=-28.5 \\ \\ y=2(x+3.5)^2 -28.5`

Answer 2

`y=2x^2+14x-4\\\\a=2;\ b=14;\ c=-4\\\\vertex\ form:y=a(x-h)^2+k\\\\where:h=(-b)/(2a)\ and\ k=(-(b^2-4ac))/(4a)\\\\h=-(-14)/(2\cdot2)=-(7)/(2)\\\\k=(-(14^2-4\cdot2\cdot(-4)))/(4\cdot2)=(-(196+32))/(8)=(-228)/(8)=-(57)/(2)\\\\\\Answer:y=2(x+(7)/(2))^2-(57)/(2)`