How do you find the vertex and axis of symmetry for #y = 4x^2 + 7#?

1 Answer
Alan P.
Aug 15, 2015

The vertex is at #(x,y) = (0,7)#
The axis of symmetry is #x=0#

Explanation:

The general vertex form for a quadratic is
#color(white)("XXXX")##y = m(x-a)^2+b#
#color(white)("XXXXXXXX")#where the vertex is at #(a,b)#

#y=4x^2+7# can easily be transformed into vertex form as:
#color(white)("XXXX")##y = 4(x-0)^2+7#
#color(white)("XXXXXXXX")#where the vertex is at #(0,7)#

The equation is that of a parabola in standard position (opening upward), so the axis of symmetry is a vertical line through the vertex
i.e. #x=0#

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