Find the points of intersection between the line y=x+7 and the curve x^2+2x+5.Also it asks to sketch the area between the graph
Points of intersection:
y = x+7
y = x^2 + 2x +5
Equate both equations
x+7 = x^2 + 2x +5
x^2 + x -2 = 0
Through factorisation: (x-1)(x+2) = 0 Hence, x = 1,-2.
Let's substitute our values of x into one of our above equations.
y=x+7
If x=1, then y=6, if x=-2, then y=5
Therefore, there are 2 points of intersection, (1,6) and (-2,5).
Graph plot: http://www.flickr.com/photos/82005243@N00/195261288/
I haven't shaded their area however. I'm sure you can do that.
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