Quadratic Functions and Equations
Main Topics
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Standard, vertex, and factored forms of a quadratic
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Graphing parabolas and identifying key features (vertex, axis of symmetry, intercepts)
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Transformations of quadratic graphs
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Solving quadratic equations (by factoring, completing the square, and the quadratic formula)
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Discriminant analysis (number and type of roots)
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Applications in projectile motion and optimization
Key Skills
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Interpret and graph quadratic functions
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Move between different forms of a quadratic equation
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Apply quadratics to real-life contexts
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Use graphing tools to verify solutions
Summary
Students explore absolute value expressions and the piecewise functions they create. They learn to graph and interpret absolute value functions and understand how they reflect symmetry in the coordinate plane. The unit also covers reciprocal functions (like y=1/xy = 1/xy=1/x and variations), exploring vertical and horizontal asymptotes and domain restrictions. These skills are critical for understanding rational and inverse relationships, which reappear in calculus.
Suggested Activities
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Graphing projects (using Desmos or graphing calculators)
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Optimization problem labs
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Vertex form transformation worksheet
