Video lecture (English) of C02 Quadratics
C02 Quadratics
What’s on the Specification
| M4.11 | Identify and interpret roots, intercepts and turning points of quadratic functions graphically. Deduce roots algebraically, and turning points by completing the square. |
| M4.16 | Solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square, and by using the quadratic formula. Know the quadratic formula: $x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ Find approximate solutions of quadratic equations using a graph. |
| MM1.3 | Quadratic functions and their graphs; the discriminant of a quadratic function; completing the square; solution of quadratic equations. |
Learning Objectives
- Fluently translate between the general, vertex, and factorised forms of a quadratic function, and use these forms to instantly identify the vertex, line of symmetry, and coordinate intercepts.
- Apply advanced factorisation techniques, such as the cross-manipulation method, to solve complex, multi-variable quadratic expressions (e.g., $ax^2+bxy+cy^2$ ).
- Master the Discriminant ($b^2-4ac$) to determine the exact number of real roots, solve quadratic inequalities, and establish strict parameter bounds (e.g., proving an expression is always positive).
- Utilise Vieta’s Formulas for quadratics to evaluate complex, symmetric expressions of roots without resorting to the quadratic formula.
- Establish root intervals by synthesising the discriminant, the axis of symmetry, and the sign of the function at specific boundary values.
- Solve higher-degree equations (such as specific quartics) by recognising “hidden quadratics” and applying strategic algebraic substitutions.
- Analyse geometric intersections between parabolas, lines, and other curves algebraically, establishing the precise conditions for tangency or distinct intersection points.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 12 | 120 min |
| Quiz | 6 | 15 min |
| Practice A | 30 | 75 min |
| Practice B | 20 | 75 min |
| Total | 68 | approx. 4-5 hrs |
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