What is the vertex of the function y=-2x2+12x-20?

Question

The problem is y= -2x(squared) +12x -20

The choices for the answer are:

(-2,20)
(-3,-74)
(2,-12)
(3,-2)

Answer 1

y = -2x² + 12x - 20
= -2(x² - 6x + 10)
= -2(x² - 6x + 9 + 1) (To complete the square)
= -2(x - 3)² - 2
So (y + 2) = -2(x - 3)²
ie (y + 2) = 4 *(-½)(x - 3)²

So vertex ≡(3, -2)

BONUS:
Focal length = -½
So focus ≡(3, -2½)
and directrix is y = -1½
and axis is x = 3

Answer 2

The x-value of the vertex is -b/2a, where y=ax^2+bx+c. So in this case, x=-12/-4=3, and when x=3, y=-2. So the answer's the last choice.

Answer 3

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Answer 4

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