### 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) = x32We will inspect the graph, the zeroes, the turning and inflection points in the cubic curve curve y = f(x).Cubic Polynomials and EquationsA 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 Characteristics of the Graph Plot, Curve Sketching 3 2 2The function given to us us f(x) = (x+20)(x+10)(x+20) = x32And the derivative2Consider the cubic equation f(x) = (x+20)(x+10)(x+20) = x32The roots of this cubic equation are at: (x - (-20)) = 0 => x = -20, ORORThis cubic equation has a double root at x = -20.The turning or stationary points is where f'(x) = 0 => 3x2These 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 factorsCheck the plot of another cubic curve hereHere's another cubic curve hereHere's another cubic curve hereCommon CoreGCSE
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Prashant Bhattacharji,
Mar 21, 2017, 1:31 AM