Quadratics and polynomial graphs.
Build quadratic equations and models with exact algebra, then connect polynomial factors with graph features.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Expanding and factorising quadratics
Connect the distributive law with reversing quadratic products, including non-monic expressions.
- 02
Solving by factorisation
Use the zero-product principle after rearranging and factorising an equation.
- 03
Completing the square
Rewrite quadratics around their turning points and solve using square form.
- 04
Quadratic formula and exact surd answers
Apply the quadratic formula and simplify exact surds before rounding.
- 05
Discriminant and the nature of roots
Predict the number of real roots and find parameter conditions using the discriminant.
- 06
Vertex/intercept/axis features
Use a parabola’s vertex, intercepts and symmetry to build a clear labelled sketch.
- 07
Converting quadratic forms
Choose expanded, factored or vertex form to reveal the feature you need.
- 08
Sum and product of roots
Use root sums and products to find coefficients and build new quadratic equations.
- 09
Building quadratic models from information
Build quadratic models from roots, a turning point or measured conditions, then interpret them.
- 10
Cubic factors and roots
Use a known cubic root to find a factor, reduce the degree and solve the remaining quadratic.
- 11
Cubic and quartic graphs and models
Read cubic and quartic shape from factors, multiplicity and leading terms, then apply simple polynomial models.
Topic review
Revisit the key ideas, then choose a practice paper.