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

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Answer 1 · 2018-04-11T01:39:04

The axis of symmetry is #x=1#.

The vertex is #(1,-6)#.

Given:

#y=x^2-2x-5# is a quadratic equation in standard form:

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

where:

#a=1#, #b=-2#, #c=-5#

Axis of symmetry: the vertical line that divides a parabola into two equal halves.

For a quadratic equation in standard form, the formula for determining the axis of symmetry is:

#x=(-b)/(2a)#

Plug in the known values and solve.

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

#x=2/2#

#x=1#

The axis of symmetry is #x=1#.

Vertex: maximum or minimum point of the parabola. Since #a>0#, the vertex will be the minimum point and the parabola will open upward.

Substitute #1# for #x# in the equation, and solve for #y#.

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

#y=1-2-5#

#y=-6#

The vertex is #(1,-6)#.

graph{y=x^2-2x-5 [-10.875, 11.625, -8.955, 2.295]}