Answer :
[tex]y=2x^2+14x-4\\\\a=2;\ b=14;\ c=-4\\\\vertex\ form:y=a(x-h)^2+k\\\\where:h=\frac{-b}{2a}\ and\ k=\frac{-(b^2-4ac)}{4a}\\\\h=-\frac{-14}{2\cdot2}=-\frac{7}{2}\\\\k=\frac{-(14^2-4\cdot2\cdot(-4))}{4\cdot2}=\frac{-(196+32)}{8}=\frac{-228}{8}=-\frac{57}{2}\\\\\\Answer:y=2(x+\frac{7}{2})^2-\frac{57}{2}[/tex]
[tex]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=\frac{-b}{2a} , \ \ \ \ k= c - \frac{b^2}{4a}[/tex]
[tex]y=2x^2+14x-4 \\ \\a=2 ,\ b=14 , \ c=-4 \\ \\ h=\frac{-14}{2*2}=-\frac{14}{4}=-3.5 \\ \\k= -4 - \frac{14^2}{4\cdot 2}=-4-\frac{196}{8}=-4-24.5=-28.5 \\ \\ y=2(x+3.5)^2 -28.5[/tex]
[tex]y=2x^2+14x-4 \\ \\a=2 ,\ b=14 , \ c=-4 \\ \\ h=\frac{-14}{2*2}=-\frac{14}{4}=-3.5 \\ \\k= -4 - \frac{14^2}{4\cdot 2}=-4-\frac{196}{8}=-4-24.5=-28.5 \\ \\ y=2(x+3.5)^2 -28.5[/tex]
