Question

Which equation could have the graph shown below? y = (x – 4)(x – 1)(2 + x)(3 + x) y = (x – 4)(1 – x)(2 + x)(3 + x) y = (x + 4)(x + 1)(2 – x)(3 – x) y = (x + 4)(x + 1)(2 – x)(x – 3)
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Answer 1

These functions are expressed in the factored form: what this means is that say for the first one y=(x-4)(x-1)(2+x)(3+x) ... when x=4, the first bracket becomes 0. Same for x=1, x=-2, x=-3 ... 

If you were to graph this, you would see that the function's line interesects the x-axis at these points... when x=4, when x=1, etc etc.

Thus, take a look at the zeroes of the graph. At which x points do they interscet the x-axis? You can determine the equation of your graph by this.