[tex]A \ quadratic \ function \ f(x) = ax^2 + bx + c \ can \ be \ expressed \ in \ the\ standard \\ form \ y = a(x - h)^2 + k \ by \ completing \ the \ square .\\ \\ Here \ the \ point \ (h, k) \ is \ called \ as \ vertex \\ \\ h=\frac{-b}{2a} , \ \ \ \ k= c - \frac{b^2}{4a} \\\\[/tex]
[tex]y=4x^{2} -8x-9 \\ \\a=4, \ \ b=-8, \ \ c=-9 \\ \\ h=\frac{-b}{2a} =\frac{8}{2\cdot 4}=\frac{8}{8}=1\\ \\k=c -\frac{b^{2}}{4a}=-9-\frac{(-8)^2}{4\cdot 4}=-9-\frac{64}{16}=-9-4=-13 \\\\y=4(x-1)^2-13[/tex]
