Quadratics and Parabolas.
Connect quadratic expressions, equations and graphs, then choose suitable methods for realistic problems.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Expanding quadratic products
Expand two linear brackets accurately and recognise square and difference-of-squares patterns.
- 02
Monic and non-monic factorisation
Factorise monic and non-monic quadratics by matching products and sums, with a final expansion check.
- 03
Zero-product equations
Use the zero-product rule to solve a quadratic equation without losing a possible root.
- 04
Completing the square
Rewrite a quadratic in square form to reveal its turning point or solve an equation exactly.
- 05
Quadratic formula
Solve a quadratic that does not factorise neatly, keeping signs, brackets and exact roots under control.
- 06
Discriminant and number of real roots
Predict the number of real roots before solving, and use that prediction to check a graph or a parameter.
- 07
Expanded, factored and vertex forms
Move between three equivalent quadratic forms and choose the one that exposes the needed information.
- 08
Roots, intercepts, symmetry and turning points
Read the main features of a parabola and connect them to its algebraic form and practical meaning.
- 09
Sketching by hand and with graphing tools
Produce a clear labelled sketch and use a graphing window that does not hide important features.
- 10
Graphical/numerical solutions
Use intersections and numerical tables to estimate solutions, and report only justified precision.
- 11
Quadratic applications and model checks
Build a quadratic from a practical situation, choose useful solutions and evaluate the model’s assumptions.
Topic review
Revisit the key ideas, then choose a practice paper.