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. y = question help: video message instructor submit question

Explanation:

Step1: Identify x - intercepts

The x - intercepts of the graph are \(x=-2\), \(x = 0\), and \(x=3\). So the factors of the polynomial are \((x + 2)\), \(x\), and \((x - 3)\).

Step2: Determine leading coefficient

As \(x\to+\infty\), \(y\to-\infty\) and as \(x\to-\infty\), \(y\to+\infty\). So the leading coefficient is \(- 1\).

Step3: Write the factored - form equation

The factored - form of the polynomial equation is \(y=-1\times x(x + 2)(x - 3)\).

Answer:

\(y=-x(x + 2)(x - 3)\)