Question

Which which equation is most likely represented by the graph above

Answer 1

The equation crosses the x axis at x=-2.5, x=0.5, x=1.5.

Since a polynomial with roots a, b, c can be written (up to factors) as

`(x-a)(x-b)(x-c)`

if we write the roots as fractions, we have

`\left(x+(5)/(2)\right)\left(x-(1)/(2)\right)\left(x-(3)/(2)\right)`

Multiply the whole expression by 2 to get

`\left(2x+5\right)\left(2x-1\right)\left(2x-3\right)`