A table of values for y=x(x+2)(x-3) is given below.

a) Calculate the values of a, b and c

Expert Answers

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Since we have x as a factor three times, we know this is going to be a 3rd degree (cubic) function, i.e., an x^3 function.  The general formula for a cubic function is ax^3+bx^2+cx+d, so we are looking for the coefficients of each power of x.

Let's do the multiplication:  (x+2)(x-3) = x^2-x-6.  Multiplying each of those terms by x, we get x(x+2)(x-3) = x^3 -x^2 -6x.  Putting it in the standard form, it will be 1x^3+(-1)x^2+(-6)x+0.  Now, we can simply read off the coefficients:  a=1, b=-1, c=-6.

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