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help graphs

south lanarkshire jag

Posted 11 November 2005 - 12:40 PM

can anyone help me with drawing the graph of 2x2(2= squared) -2x?

thanks

SLJ

*sofax*

Posted 11 November 2005 - 12:42 PM

what's the equation I'm confused by the way you have written it! smile.gif

south lanarkshire jag

Posted 11 November 2005 - 01:04 PM

(2x) all squared Subtract 2x

it's for a friend

*sofax*

Posted 11 November 2005 - 02:00 PM

with the x being squared it sounds to me like it should be an up right parabola! smile.gif

aldo

Posted 11 November 2005 - 03:05 PM

You can use software such as Excel (or your calculator) taking set values of x and calculating the corresponding y value.

I have attached what it should look like.



dfx

Posted 11 November 2005 - 06:12 PM

Just a quick run through of teh sketching procedure:

 y = 2x^2 - 2x = 2x(x-1) implies.gif x = 0 or x = 1.

So now you know it cuts the x-axis through 0 and 1.

It cuts the y-axis when x = 0, so y = 0 also.

Lastly, find the turning points by differentiating and setting the derivative = 0.

 \displaystyle {\frac {dy}{dx}} = 4x - 2

At turning points, \displaystyle {\frac{dy}{dx}} = 0 

4x - 2 = 0 so x = 1/2

So the x-coordinate of the turning point is x = 1/2 . For the y-coordinate:

 y = 2x^2 - 2x = 2 (1/2) ^2 - 2 (1/2) = -1/2

So the turning point is (1/2 , -1/2).

Finally, you know its a parabola because it's a degree 2 polynomial, and that it has a minimum turning point (i.e. it's U shaped because the coefficient of x power2.gif is positive).

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