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Find the vertex of this parabola: y=-4x^2+8x-12

User Noremac
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2 Answers

3 votes
(1,-8) is the vertex
User Zoe Edwards
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8.3k points
2 votes
The vertex of the parabola is the highest or lowest point of the graph.

y=-4x^2+8x-12 = -4 (x^2 -2x +3)

Lets work with this now:
x^2 -2x +3

x^2 -2x +3 -> what is the closeset perfect square?
x^2 -2x +1 = (x-1)^2
So
x^2 -2x +3 = (x-1)^2 +2

Replacing to original
y=-4x^2+8x-12 = -4 (x^2 -2x +3) = -4 ((x-1)^2 +2) = -4 (x-1)^2 - 8

The min or max point is where the squared part = 0
So when x=1 , y= -4*0-8=-8

This will be the max of the parabola as there is - for the highest factor (-4x^2)

The max: x=1, y= -8
User Herr
by
8.6k points

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