What is the axis of symmetry and vertex for the graph #y = 2x^2 + 7x -5#?

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Answer 1 · 2017-02-16T08:39:38

The axis of symmetry is #x=-7/4#
The vertex is #V=(-7/4,-89/8)#

In order to write the equation in the vertx form, we need to complete the squares

#y=2x^2+7x-5#

#y=2(x^2+7/2x)-5#

#y=2(x^2+7/2x+color(red)(49/16))-5-color(blue)(49/8)#

#y=2(x+7/4)^2-89/8#

The axis of symmetry is #x=-7/4#

and the vertex is #V=(-7/4,-89/8)#

graph{(y-(2x^2+7x-5))(y-1000(x+7/4))=0 [-27.8, 23.5, -18.58, 7.1]}