Topic 16 · Number & Algebra
Quadratics
Expanding, factorising and solving quadratics, sketching their graphs, and where a line meets a curve.
By the end of this topic you can…
- Recognise the shape of a quadratic graph
- Expand the product of two brackets
- Factorise a quadratic expression
- Solve a quadratic equation by factorising
- Solve a line and a curve simultaneously, using the discriminant to count the points of intersection
- Sketch a quadratic graph from its roots, y-intercept and turning point, completing the square
Lessons
- Graphs of Quadratics Tables of values for , the shape of a parabola, and what , and do to it.
- Expanding Products of Brackets Expanding , products with two letters, and the perfect-square and difference-of-two-squares patterns.
- Factorising Quadratic Expressions Reversing expansion: finding two numbers that multiply to the constant and add to the coefficient.
- Solving Quadratic Equations Solving by factorising, forming quadratics from word problems, and trial and improvement when factorising will not work.
- Non-linear Simultaneous Equations Where a straight line meets a parabola, a circle or another curve: forming one quadratic equation, using the discriminant to count — or control — the points of intersection, and solving to find them, with the formula when it will not factorise.
- Sketching Quadratic Graphs Sketch any parabola without a table of values: find where it crosses the axes, decide its shape, and complete the square to find the turning point — then check it sits on the line of symmetry.
Quadratics quiz
Ten questions drawn at random from a bank of twelve, covering graphs, expanding, factorising and solving quadratics. This is an extension topic.
10 questions · pass mark 70%