Answer:
[tex]f(x)=-x(x+2)(x-1)^2[/tex]
Step-by-step explanation:
From inspection, the curve has 3 turning/stationary points, which suggests it is quartic function. In factored form: ax(x + b)(x + c)(x + d)
From inspection, there are 3 roots at: [tex]x = -2, x = 0, x = 1[/tex]
Therefore x, (x + 2) and (x - 1) will be factors.
Whenever a turning/stationary point touches the x-axis, we conclude that a root is repeated at that point. Therefore, from inspection, root x = 1 is a repeated root. So x, (x + 2) and (x - 1)² are factors.
The quartic curve is a "n" shape, which means the leading coefficient is negative. We are told the leading coefficient is + or - 1. Therefore, it will be -1.
Therefore, an equation for the function in factored form is:
[tex]f(x)=-x(x+2)(x-1)^2[/tex]
