Lesson Notes By Weeks and Term v4 - SHS 3
PATTERNS AND RELATIONS
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PATTERNS AND RELATIONS
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Subject: Mathematics
Class: SHS 3
Term: 1st Term
Week: 10
Grade code: 3.2.2.LI.2
Strand code: 2
Sub-strand code: 2
Content standard code: 3.2.2.CS.1
Indicator code: 3.2.2.LI.2
Theme: ALGEBRAIC REASONING
Subtheme: PATTERNS AND RELATIONS
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This lesson focuses on understanding and visualising quadratic functions by drawing their graphs. Have you ever wondered about the path a football takes when kicked, the shape of the Adomi Bridge arch, or how a small business owner can determine the price that gives them the most profit? These real-world situations can be modelled by a special U-shaped curve called a parabola, which is the graph of a quadratic function. By learning to draw these graphs, we can visually solve equations and find important points, like the highest height a ball reaches or the point of maximum profit.
Starter: Review of Linear Graphs (Talk for Learning - 10 mins)
Let's quickly recall. A linear equation like `y = 2x + 1` always produces a straight line when graphed. We only need two points to draw it. However, today we are looking at equations with an `x²` term. These behave very differently. A. The Quadratic Function
A quadratic function is any function that can be written in the standard form: `y = ax² + bx + c` where `a`, `b`, and `c` are constants, and `a ≠ 0`. The `x²` term is what makes it "quadratic," and it is responsible for the curved shape of the graph.
The graph of a quadratic function is a smooth, symmetrical U-shaped curve called a parabola. B. Shape of the Parabola: Maximum vs. Minimum Point