By the end of this course, students will…
- make connections, through investigation using graphing technology (e.g., dynamic geometry software), between a polynomial function given in factored form [e.g., f(x) = 2(x –3)(x + 2)(x –1)] and the x-intercepts of its graph, and sketch the graph of a polynomial function given in factored form using its key features (e.g., by determining intercepts and end behaviour; by locating positive and negative regions using test values between and on either side of the x-intercepts)
- Investigate, using graphing technology, the x-intercepts and the shapes of the graphs of polynomial functions with one or more repeated factors, for example, f(x) = (x –2)(x –3), f(x) = (x –2)(x –2)(x –3), f(x) = (x –2)(x –2)(x –2)(x –3), and f(x) = (x+2)(x+2)(x –2)(x –2)(x –3), by considering whether the factor is repeated an even or an odd number of times. Use your conclusions to sketch f(x) = (x +1)(x +1)(x –3)(x –3), and verify using technology.
By the end of the lesson, students will…
- Determine the degree of a polynomial function in factored form
- Be able to graph various polynomial functions by looking at their factored form
- I can use a factored equation to draw a graph of a polynomial
For extra practice, print out the handout below and complete all parts of questions 3 and 4. To check your work, head over to desmos.com or download the desmos app. This application allows you to input any function and see it’s graph.