1 / 7

Graphing Cubic Polynomials

Identify various types of cubic curves (Refer to Excel Applet for Cubic Curves) Sketch simple cubic curves Form equation of cubic polynomial from sketch. Graphing Cubic Polynomials. Graphing Cubic Polynomials.

toril
Download Presentation

Graphing Cubic Polynomials

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Identify various types of cubic curves (Refer to Excel Applet for Cubic Curves) Sketch simple cubic curves Form equation of cubic polynomial from sketch Graphing Cubic Polynomials

  2. Graphing Cubic Polynomials The real roots of the polynomial equation P(x) = 0 are given by the values of the intercepts of the function y = P(x) with the x-axis. Nature of roots: 3 real and distinct  x = x1, x = x2 and x= x3 are the solutions. 2 real and equal and 1 real and distinct 1 real and 2 complex roots

  3. 10 5 0 -4 -2 0 2 4 -5 -10 Definition of Cubic Function A cubic function is a polynomial function of the form ax3 + bx2 + cx + d, where a, b, c and d are constants and a cannot be 0. Example 1: y = x3

  4. 10 5 0 -4 -2 0 2 4 -5 -10 Use the excel applet to investigate Example 2: y = x3 – 5x2 + 2x + 8

  5. 10 5 0 -2 -1 0 1 2 3 4 -5 -10 Use the excel applet to investigate Example 3: y = x3 – x2 - x +1

  6. Graphing Cubic Polynomials How to graph a cubic function? Example : y = x3 – 2x2 –x + 2 (Note: a > 0) Step 1: Check if y can be factorise into 3 linear factors y = (x + 1)(x -2)(x -1) (Sometimes, you may get 1 linear factor and a quadratic factor that cannot be factorised When this happens – use the quadratic formula to solve for x. If it cannot be solved, then there will be 2 complex roots and 1 real root) Step 2: Set y = 0, x = -1, x = 2, x = 1

  7. y = x3 – 2x2 –x + 2 Graphing Cubic Polynomials Step 3: Finding the y-intercept. When x = 0, y = 2.  (0, 2)

More Related