Question

Determine an equation for the pictured graph. Write your answer in factored form and assume

the leading coefficient is either 1 or -1, you should be able to determine which is the case by
looking at the graph.

Answer 1

After examining the curve, it can be observed that there are three points where it turns or remains stationary. This indicates that the function is likely a quartic function that can be expressed in factored form as ax(x + b)(x + c)(x + d). By inspecting the curve, it can be determined that the function has three roots at x=-2, x=0, and x=1. Thus, the factors of the function will be x, (x+2), and (x-1).

Since a turning/stationary point touching the x-axis indicates a repeated root, it can be concluded that the root at x=1 is repeated. Therefore, the factors will be x, (x+2), and (x-1)^2.

As the quartic curve has an "n" shape, the leading coefficient of the function must be negative. The problem states that the leading coefficient is either positive or negative one, so the leading coefficient must be -1.

Thus, the equation for the function in factored form will be f(x)=-x(x+2)(x-1)^2