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Learning intentions:
In this section we will examine:
- How to expand and factorise quadratics.
- Solving quadratic equations by factorising, completing the square and using the general quadratic formula.
- Using the discriminant to determine the number of solutions for a quadratic equation.
- Graph quadratic functions in general form, turning point form or factorised form.
- Solving quadratic inequalities.
- Solving simultaneous equations involving a quadratic and a linear function.
- Determining the rule of a quadratic function.
- Applications and modelling of problems with quadratic functions.
Introduction:
Section 4 introduces quadratic functions. A quadratic function is a polynomial with the highest power (n) being 2. The graph of a quadratic is a parabola. There are three important forms that a quadratic equation can be expressed in:
- The general form of a quadratic equation is:
Contents:
- 4A - Expanding quadratics
- 4B - Factorising quadratic trinomials
- 4C - Solving quadratic equations
- 4D - The general quadratic formula
- 4E - The discriminant (Δ)
- 4F - Completing the square
- 4G - Graphing quadratic functions
- 4H - Solving quadratic simultaneous equations
- 4I - Solving quadratic inequations
- 4J - Determining the rule of a quadratic
- 4K - Applications and modelling with quadratics
- Section 4 - Resources
- The turning point form of a quadratic equation (with turning point (h,k)) is:
- The factorised form of a quartic equation (where the x-intercepts occur at (b,0) and (a,0) is:
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