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How do I sketch the graph of this function?

I can do the ones that are like:

(x-3)(x+2)(x-4)

But now I have:

(x-2)(x^2+x+1)

, and I don't know what to do.

Would starting by doing this be right?:

(x-2)(x^2+x+1)

(x-2)((x+\frac{1}{2})^2-\frac{1}{4}+\frac{4}{4})

(x-2)((x+\frac{1}{2})^2-\frac{3}{4})

Reply 1

n_251

yup looks good...you basically should make each bracket equal 0...so you want to find the values of x when

x^2 + x + 1 = 0

Completing the square (like you have done) is one way of doing this and for this particular example I would do this but I don't think you can get real roots for

x^2 + x + 1 = 0

. So this particular example is not the best!

Reply 2

Pheylan

http://www.wolframalpha.com/input/?i=y%3D%28x-2%29%28x^2%2Bx%2B1%29

Reply 3

miml

I would just use calculus to find the turning points (and their nature), and also the fact that it has a root at x=2

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