Thread: help please

4. Function p is described as p(x) = (x – 2)(4 – x)(x + 1).
What is the order of function p and what name describes this type of polynomial?
What is the constant term of function p?
Sketch the curve y = p(x) showing clearly the coordinates of the points where the curve meets both the axes.

Originally Posted by Koops

4. Function p is described as p(x) = (x – 2)(4 – x)(x + 1).
What is the order of function p and what name describes this type of polynomial?
What is the constant term of function p?
Sketch the curve y = p(x) showing clearly the coordinates of the points where the curve meets both the axes.

1. The degree is three. It's a cubic. Google that term to find many examples.

2. Partially expand it to see the constant term: (-2)(4)(1) = -8.

3. Use the null factor law to get the x-intercepts. Substitute x = 0 to get the y-intercept (you will, unsurprisingly, y = -8). Be careful with the shape ..... Note that as x --> +oo, y --> -oo and as x --> -oo, y --> +oo.