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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
when x = 1.5
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.
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