Question

Given the equation:

y=−2 x2

−12x−23
Find the parabola's vertex.

Answer 1

-b / 2a = 12 / -4 = -3;
-Δ / 4a = - ( 144 - 184 ) / -8 = 40 / -8 = -5

Answer 2

`y=-2x^2-12x-23 \\ \\a=-2 ,\ b=12,\ c=-23 \\ \\ vertex(h, k) \ is \ given \ by: \\ \\h = (-b)/(2a) , \ \ k = \frac {-\Delta }{4a }`


`\Delta =b^2-4ac = 12^2-4\cdot(-2) \cdot (-23)=144-184=-40`


`h=( 12)/(2\cdot (-2))=(12)/(-4)=-3 \\ \\k=(40)/(4\cdot (-2))=(40)/(-8)=-5 \\ \\Answer : \ vertex \ \ (-3,-5)`