What is the axis of symmetry and vertex for the graph #y = 2x^2 + 24x + 62#?

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Answer 1 · 2017-08-24T18:17:16

The axis of symmetry is #-6#.

The vertex is #(-6,-10)#

Given:

#y=2x^2+24x+62# is a quadratic equation in standard form:

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

where:

#a=2#, #b=24#, and #c=62#.

The formula for finding the axis of symmetry is:

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

Plug in the values.

#x=-24/(2*2)#

Simplify.

#x=-24/4#

#x=-6#

The axis of symmetry is #-6#. It is also the #x# value for the vertex.

To determine #y#, substitute #-6# for #x# and solve for #y#.

#y=2(-6)^2+24(-6)+62#

Simplify.

#y=2(36)+(-144)+62#

#y=72-144+62#

#y=-10#

The vertex is #(-6,-10)#.