Question

PLEASE PLEASE PLEASE HELP Determine an equation for the pictured graph. Write your answer in factored form and assume the leading coefficient is...

Answer 1

Answer:

$f(x)=-x(x+2)(x-1)^2$

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: $x = -2, x = 0, x = 1$

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:

$f(x)=-x(x+2)(x-1)^2$