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Given the equation:
y=−2x2−12x−23
Find the parabola's vertex.

Sagot :

crisforp
-b / 2a = 12 / -4 = -3;
-Δ / 4a = - ( 144 - 184 ) / -8 = 40 / -8 = -5
Lilith
[tex]y=-2x^2-12x-23 \\ \\a=-2 ,\ b=12,\ c=-23 \\ \\ vertex(h, k) \ is \ given \ by: \\ \\h = \frac{-b}{2a} , \ \ k = \frac {-\Delta }{4a }[/tex]

[tex]\Delta =b^2-4ac = 12^2-4\cdot(-2) \cdot (-23)=144-184=-40[/tex]

[tex]h=\frac{ 12}{2\cdot (-2)}=\frac{12}{-4}=-3 \\ \\k=\frac{40}{4\cdot (-2)}=\frac{40}{-8}=-5 \\ \\Answer : \ vertex \ \ (-3,-5)[/tex]




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