MYP 4Year 10Term 2
Quadratic Equations
Factorising · Completing the square · Quadratic formula
Algebra
15 objectives
Learning objectives
What students should be able to do by the end of this unit.
Solving Quadratic Equations
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- Solve a quadratic equation by factorising and applying the null factor law.
- Solve a quadratic equation of the form $x^2 = k$ or $(x - a)^2 = k$.
- Solve rational equations that reduce to a quadratic after clearing fractions.
- Complete the square to solve a quadratic equation.EXT
- Solve a quadratic equation using the quadratic formula $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.EXT
- Give exact (surd) solutions to quadratic equations where appropriate.EXT
Graphs of Quadratic Functions
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- Identify the $y$-intercept of a quadratic function as $f(0)$.
- Find the $x$-intercepts (roots) of a quadratic by setting $f(x) = 0$.
- Determine the axis of symmetry and the vertex (maximum or minimum) of a quadratic.
- Sketch a quadratic from its key features (intercepts, vertex, direction of opening).
- Convert between expanded, factorised and vertex forms of a quadratic.EXT
Applications and Discriminant (Extended)
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- Solve optimisation problems modelled by a quadratic (e.g. maximum area, maximum profit, projectile motion).
- Solve a system consisting of a linear and a quadratic equation algebraically.
- Use the discriminant $b^2 - 4ac$ to determine the nature of the roots (two distinct, one repeated, none).EXT
- Solve quadratic inequalities using a sketch or sign-table.EXT
Review pack
Curated revision materials parents and students can download.
A review pack for this unit is being prepared.