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

Answer 1

Abigail Allen

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]}

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Answer 2

Abigail Allen

The axis of symmetry for the graph ( y = 2x^2 + 7x -5 ) is ( x = -\frac{7}{4} ). The vertex of the graph is ( \left( -\frac{7}{4}, -\frac{67}{8} \right) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.