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. Here is a tutorial on Quadratic Equations, Cubic and Higher Order Equations - Using Factorization and Formula- A tutorial with solved problems and a Quiz Graph of y = f(x) = (x+20)(x+10)(x+20) = x32  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, OR OR 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 |
The Learning Point > Mathematics > Graphs of Cubic Polynomials, Curve Sketching and Solutions to Simple Cubic Equations >
