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

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Answer 1 · 2015-07-18T22:32:45

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

#y = -x^2+1#

The standard form of the equation for a parabola is

#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 [-3, 3, -5, 2]}