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: 14
Grade code: 3.2.2.LI.3
Strand code: 2
Sub-strand code: 2
Content standard code: 3.2.2.CS.1
Indicator code: 3.2.2.LI.3
Theme: ALGEBRAIC REASONING
Subtheme: PATTERNS AND RELATIONS
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This lesson explores the visual properties of quadratic functions, specifically their graphs, which are called parabolas. We see these shapes all around us in Ghana – from the arc of a football kicked at the Accra Sports Stadium to the shape of the Adomi Bridge supports. By understanding the properties of these graphs, like the axis of symmetry, and how they interact with straight lines, we can solve complex real-world problems related to maximum heights, projectile paths, and economic modelling. This lesson will equip learners with the graphical skills to analyse and solve systems of equations involving both quadratic and linear functions.
Part 1: The Quadratic Graph (Parabola) and its Axis of Symmetry
A quadratic function is a function of the form y = ax² + bx + c, where 'a', 'b', and 'c' are constants and 'a' is not zero. The graph of a quadratic function is a smooth, U-shaped or n-shaped curve called a parabola. If a > 0 (positive), the parabola opens upwards (like a smile 😊). If a < 0 (negative), the parabola opens downwards (like a frown ☹️).
What is the Axis of Symmetry?
The axis of symmetry is a vertical line that divides the parabola into two perfect, mirror-image halves. If you were to fold the graph along this line, the two sides would match up exactly. Because it is a vertical line, its equation is always in the form x = k, where 'k' is a constant. The axis of symmetry passes through the vertex (the minimum or maximum point) of the parabola.