Online assignments = confusion!

1. Mar 5, 2009

Alana456

I'm doing an online course, and am finding it to be extremely difficult to do without having an actual teacher that you can sit with and a classroom full of others you can work with.

1. One of the questions is:
Determine a general equation for the quartic function f(x) as described:
f(x)<0 when x< -2, f(x)>0 when -2<x<3, and f(x)<0 when x>3, the zeros are -2, -1, and 3.

I've never worked with quartic functions or anything like this.
If anyone has some guidance that would be fantastic!!!

2. Mar 5, 2009

Mentallic

It's not much more than just an extension from quadratics/cubics.
The general form is $$y=ax^4+bx^3+cx^2+dx+e$$ but this wont help much in this case.
Using the fact that for a quartic in the form $$y=a(x-b)(x-c)(x-d)(x-e)$$, the roots are $$b, c, d, e$$ so since you know the roots are -2,-1 and 3, It can be written as $$y=(ax+b)(x+2)(x+1)(x-3)$$
Now just see if you can add anything from the other info given. Such as finding whether a is positive or negative (the coefficient of the highest power ($$x^4$$) is important such as how it makes quadratics concave up or concave down).

3. Mar 6, 2009

HallsofIvy

Staff Emeritus
Because "f(x)>0 when -2<x<3", the graph of f does not cross the x axis at x= -1. But x= -1 is a zero so the graph must be tangent to the axis there. That means x= -1 is a double root" the four[/b roots are -2, -1, -1, 3, and so gives you the fourth factor that Mentallic writes as "ax+ b".