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How do you find the vertex of a parabola #y=-[x]^2+1#?

Answer 1

Isaiah Anthony

The vertex is at #color(red)((0,1)#.

#y = -x^2+1#

The equation for a parabola is written in standard form as

#y = ax^2+bx+c#, so

#a = -1#, #b = 0#, #c = 1#

The #x#-coordinate is at #x = -b/(2a) = -0/(2(-1)) = 0#

To find the #y#-coordinate of the vertex, substitute #x =0# into the equation to get

#y = -(0)^2 +1 = 0+1 = 1#

The vertex is at (#0,1#).

graph{-x^2+1 [-5, 2, 3, 3, -3]}

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Answer 2

Eva Abramson

To find the vertex of the parabola with the equation (y = -|x|^2 + 1), first, identify that the graph is a downward-facing parabola. The vertex of this parabola is at the point (0, 1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.