What is the axis of symmetry and vertex for the graph #2(y - 2) = (x + 3)^2#?

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Answer 1 · 2016-11-21T19:15:34

The vertex is at #(-3, 2)# and the axis of symmetry is #x = -3#

Given: #2(y - 2) = (x + 3)^2#

The vertex form for the equation of a parabola is:

#y = a(x - h)^2 + k#

where "a" is coefficient of the #x^2# term and #(h, k)# is the vertex.

Write the (x + 3) in the given equation as (x - -3):

#2(y - 2) = (x - -3)^2#

Divide both sides by 2:

#y - 2 = 1/2(x - -3)^2#

Add 2 to both sides:

#y = 1/2(x - -3)^2 + 2#

The vertex is at #(-3, 2)# and the axis of symmetry is #x = -3#