Question 331599: graph: y= x^2 + 5x + 6
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! This is a parabola in general form. The easiest way to graph it is to turn it into standard form [y=a(x-p)^2+q], by completing the square.
y=x^2 +5x+6
Halve the b term (b=5 in this equation), then square it. (5/2)^2 = 25/4
Add this number to the first two terms, but then subtract it from the end (so that you are only adding zero to the equation).
y = x^2 +5x +25/4 +6 -25/4
y = (x+5/2)^2 -1/4
You can now see where the parabola is. It is at (p,q) = (-5/2, -1/4)
Plot this point, then draw a parabola, opening up from that point. Follow the same trend as normal, with y=x^2 as your guide.
Example, go right/left 1, up 1. right/left 2, up 4, right/left 3, up 9, right/left 4, up 16... and so on.
Here's a graph of your parabola: http://www.wolframalpha.com/input/?i=y+%3D+(x%2B5/2)^2+-1/4
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