Graph of Cubic Functions/Cubic Equations for zeros and roots (-20,-10,-20)

Let us consider the cubic function f(x) = (x+20)(x+10)(x+20) = x32
We will inspect the graph, the zeroes, the turning and inflection points in the cubic curve curve y = f(x).

Cubic Polynomials and Equations

A cubic polynomial is a polynomial of degree 3.
where a is nonzero.
An equation involving a cubic polynomial is called a cubic equation and is of the form f(x) = 0. There is also a closed-form solution known as the cubic formula which exists for the solutions of an arbitrary cubic equation. A cubic polynomial is represented by a function of the form. And f(x) = 0 is a cubic equation. The points at which this curve cuts the X-axis are the roots of the equation.

Graph of y = f(x) = (x+20)(x+10)(x+20) = x32
Cubic Polynomial Curve Plot on Graph

Characteristics of the Graph Plot, Curve Sketching

3 2
The function given to us us f(x) = (x+20)(x+10)(x+20) = x32
And the derivative2

Consider the cubic equation f(x) = (x+20)(x+10)(x+20) = x32
The roots of this cubic equation are at: 
(x - (-20)) = 0 => x = -20, 
This cubic equation has a double root at x = -20.

The turning or stationary points is where f'(x) = 0 => 3x2
These are also called the "critical" points where the derivative is zero. 
Coming to other geometrical features of this curve: What we see here is the graph of a nonlinear function. The y-intercept of this curve is at y=4000.

If we know the zeroes, then we can write down algebraic expressions for the coefficients. Going the other way is much harder and cannot be done in general.
A cubic function has a bit more variety in its shape than the quadratic polynomials which are always parabolas. We can get a lot of information from the factorization of a cubic function. We get a fairly generic cubic shape when we have three distinct linear factors

Check the plot of another cubic curve here

Here's another cubic curve here

Here's another cubic curve here
Common CoreGCSE

Prashant Bhattacharji,
Mar 21, 2017, 1:31 AM