Question

Write the equation of the graph shown below in factored form.

a graph that starts at the top left and continues down through the x axis at negative one to a minimum around y equals negative one and goes up to touch the x axis one and then goes back down to a minimum around y equals negative four and goes back up through the x axis at three.

f(x) = (x − 1)2(x - 1)(x + 3)
f(x) = (x − 1)2(x + 1)(x − 3)
f(x) = (x + 1)2(x + 1)(x + 3)
f(x) = (x − 1)2(x − 1)(x − 3)

Answer 1

f(x) = (x − 1)^2(x + 1)(x − 3)

Answer 2

Look at where the red line crosses/ touches the X axis. This will give you the zeros.

It crosses at -1, it touches at 1 and crosses again at 3

This means the zeros are -1, 1 and 3

So you now you need to have (x+1) (x-3) and (x-1) as factors.

This makes the answer: f(x) = (x − 1)2(x + 1)(x − 3)