Lesson Notes By Weeks and Term v4 - SHS 1

Lesson Video

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Performance objectives

• Draw graphs of polynomial functions up to degree 3.
• Identify key features like turning points and axis of symmetry.
• Solve problems using graphs of polynomial functions.
• Analyze how changing a function affects its graph.

Lesson summary

This lesson introduces the powerful technique of using graphs to understand and solve algebraic problems. We move beyond simply finding 'x' to visualizing the behaviour of functions. Polynomials are not just abstract equations; they model real-world phenomena, from the arc of a football kicked at the Accra Sports Stadium to the profit curve of a small business selling "bofrot" in Makola Market. By learning to draw and interpret these graphs, we gain a visual tool for problem-solving, which is often more intuitive than pure algebra.

Lesson notes

2.1 What are Polynomial Functions? A polynomial function is an expression involving a sum of powers in one or more variables multiplied by coefficients. For this lesson, we are focusing on polynomials in one variable, `x`. Linear Function (Degree 1): `f(x) = mx + c`. The graph is a straight line. Quadratic Function (Degree 2): `f(x) = ax² + bx + c`. The graph is a parabola (a 'U' or 'n' shape). Cubic Function (Degree 3): `f(x) = ax³ + bx² + cx + d`. The graph is a curve that typically has an 'S' shape.

The "degree" is the highest power of `x` in the function. 2.2 Drawing Quadratic Functions (Parabolas) by Hand

Let's learn the step-by-step process by drawing the graph of `f(x) = x² - 2x - 3` for the interval `-2 ≤ x ≤ 4`.

Step 1: Create a Table of Values We choose integer values for `x` from -2 to 4 and calculate the corresponding `f(x)` or `y` value for each.

Evaluation guide

• Draw the graph of a polynomial function with degrees up to 3 by hand and by using
• technology (e.g., GeoGebra, Demos, PhET Simulations, and Geometer’s Sketch Pad)
• where appropriate.
• Use graphs of polynomial functions to solve problems.