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 Question from anamika, a student: number of solutions of sinx = x^2 + x +1 graphically?

Hi Anamika,

I would first sketch $y = \sin x.$

Now consider $y = x^2 + x + 1.$ The function is a quadratic so the graph is a parabola which either opens upwards or downwards. Which is it?

Plot a few points on the graph of $y = x^2 + x + 1,$ for example $x = 0, x = 1 \mbox{ and } x = -1.$ Sketch the graph of $y = x^2 + x + 1.$ How many points lie on both graphs?

Penny

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