Sketching a cubic function

label Algebra
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1. Sketch the graph of y = (x - 2)(x + 4)(x - 1)

I can tell how to put these coordinates in, but do I need a calculator to sketch this? if not, how do I sketch this without a calculator, and how can I tell how high up the curves go?

Aug 25th, 2015

Thank you for the opportunity to help you with your question!

To sketch the above graph you may or may not need a calculator depending on your mathematical prowess.

However if you have knowledge in basic addition , subtraction and multiplication you do not need a calculator.

To sketch the above graph you need to randomly select 5 or more values of x and use the equation to get the corresponding values of y.

my x values will be 1, 1.5, 2 , 2.5, 3,4, 5

when x =1 y will be

y =(1-2)(1+4)(1-1)

y =0

when x = 1.5

y =1.5-2)(1.5+4)(1.5-1)

y = -0.5*5.5*0.5  (For this you might need a calcuator) = 1.375

when x= 2

y = (2-2)(2+4)(2-1) = 0

You can do the same for the other values of x and get the corresponding values of y. With the points you get you can then sketch the graph.

To determine ho high the graph goes you can either sketch it or use differential calculus to determine maxima.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 25th, 2015

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