sketch the graph of y=2x^2-12x+5 by completing the square and making appropriate transformations of y=x^2

Question

sketch the graph of y=2x^2-12x+5 by completing the square  and making appropriate transformations of y=x^2

mathmate · Answer

y=2(x-3)^2-13
So the graph has its vertex at (3,-13), and y-intercept +5.  The zeroes are at 3+/-sqrt(6.5)

anonymous · Answer

can you explain how you did that?

mathmate · Answer

y=2(x-3)^2-13
is obtained by completing the squares.
The y-intercept is from the constant term of the original expression.
The zeroes are from solving 2(x-3)^2-13=0

anonymous · Answer

The sketch of the graph should look something like the attachment.

mathmate · Answer

Oh, I forgot to mention, the graph is concave upwards, which is obtained by the positive value of +2 of the leading coefficient (2x^2+...)

Hi Rob: Maybe it's computer glitch, but I don't see much in the attachment.

anonymous · Answer

Very strange.  The attachment is a Mathematica generated plot of 2x^2-12x+5 between x=0 and x=6 which is definitive ie: Far beyond a human generated sketch.  Adjust your PDF viewer so that the you can see the entire curve showing the vertex is at about (3,-13) and the y intercept at (0,5).

mathmate · Answer

Thanks for you info.  For some reason it displays now.  Probably my old workhorse took a coffee break.  It IS a very nice plot.

anonymous · Answer

I'm glad that you are convinced.  Have a good day.

mathmate · Answer

Same to you too!