D asked in Science & MathematicsMathematics · 7 years ago

# Maths: polynomial graphs?.?

Maths: polynomial graphs?

3. Suppose that f(x) has (x -2)^2 and (x + 1) as its only factors.



a) Sketch the graph of f.

b) State all the zeros of f.

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• 7 years ago

In reverse order,

b) The only zeros of f are where the factors equal zero, namely at x = - 1 and x = 2

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a) Since those are the only given factors, the polynomial (in unexpanded form) is :

p(x) = (x - 2)^2 * (x + 1)

From there, choose simple values of x and make a quick table of points, plot them, and draw a smooth curve through them. (Which sounds easy enough, but the 'problem' with cubic functions like this one is that they grow quickly, and so you have to give thought to what scale to use on your graph. It's simple nowadays thanks to graphing calculators.)

x . . . . . . p(x)

- 3 . . . . . - 50

- 2 . . . . . - 16

- 1 . . . . . . 0

0 . . . . . . . 4

1 . . . . . . . 2

2 . . . . . . . 0

3 . . . . . . . 4

4 . . . . . . . 20

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Here's what it should look like:

(coordinate axes are not the same scale)

http://s1164.photobucket.com/albums/q561/iago9/?ac...