How do you identify the important parts of # y = 2x^2 - 10x - 1# to graph it?

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Answer 1 · 2015-09-29T15:16:09

Vertex #(5/2, 23/2)# and axis of symmetry is #x=5/2#

This is a quadratic function, hence it represents a parabola. Important parts to identify is its vertex and the axis of symmetry.

This is done by completing the square for x, as shown below:

#y= 2(x^2 -5x) -1#

#y=2( x^2 -5x +25/4 -25/4)-1#

#y=2(x-5/2)^2 +25/2 -1#

#y=2(x-5/2)^2 +23/2#

This gives vertex #(5/2, 23/2)# and axis of symmetry is #x=5/2#