What is the axis of symmetry and vertex for the graph #y=-x^2+2x-5#?

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Answer 1 · 2016-06-16T09:51:06

#x= 1 # is the line of symmetry and the vertex is at #(1,-4)#

This is the equation of a parabola with the standard form

#y = ax^2 + bx + c#

To find the axis of symmetry (a vertical line), use the formula:
#x = (-b)/(2a)#.

This will give you the x-value which is exactly in the middle of the parabola.

#x = (-2)/(2xx-1) = (-2)/(-2) = 1#

The vertex (or turning point) lies on the axis symmetry.

So, if #x = 1,# then find the #y# value by substituting into the original equation

#y = -(1)^2 + 2(1) - 5#

#y = -1 +2 -5 = -4#

So the vertex is at (1 -4)