
Ready-to-teach resources for the full quadratics unit — factoring, the quadratic formula, completing the square, and graphing parabolas. Built for senior algebra classrooms with worked examples, structured practice, and assessment-style problems your students can work through independently.
Worked examples for every solution method — factoring trinomials, applying the quadratic formula, and completing the square — so your class sees the same problem solved three ways and learns when to choose each approach.
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Real-world applications that make quadratic functions click — projectile motion, maximum profit, optimising areas, and bridge-arch geometry. Every applied problem comes with full solutions and discussion prompts.
Graphing sequences move from plotting tables of values, to identifying transformations, to sketching from vertex form. Each worksheet pairs a skills page with an application page so practice and reasoning happen side by side.

Graphing practice covering vertex form, axis of symmetry, intercepts, and the effect of changing coefficients on the shape of a parabola — with printable grids and exemplar graphs for marking.
Each lesson scaffolds from the standard form ax² + bx + c through to identifying roots, the discriminant, and the vertex. Students build fluency through guided practice before moving to mixed problem sets.
Applied tasks help students see why quadratic functions matter beyond the textbook. Worked solutions explain the modelling assumptions so teachers can run rich classroom discussions without extra prep.
- You in approximately four minutes
Factoring and Solving Quadratic Equations
The Quadratic Formula and Completing the Square
Graphing Quadratic Functions and Parabolas
The factoring resources move students through GCF, difference of two squares, and trinomial factoring — including the AC method for non-monic quadratics. Worked examples show every step, followed by graded practice from straightforward equations through to problems requiring rearrangement before factoring. Solution sets cover the null-factor law and how to interpret the two roots in context, giving students a clear path from algebraic manipulation to the meaning of a solution.
When a quadratic will not factor cleanly, students need the formula and completing-the-square method in their toolkit. These resources derive the quadratic formula from completing the square, then drill substitution, simplification, and surd answers. The discriminant is treated as a standalone skill — students learn to predict the number and nature of roots before solving. Mixed problem sets push students to choose the most efficient method for each equation rather than defaulting to one.
Graphing resources cover vertex form, factored form, and standard form — and how to convert between them. Students learn to identify the axis of symmetry, the vertex, the y-intercept, and the x-intercepts directly from each form, then sketch parabolas without plotting every point. Applied problems link the graph back to real contexts: projectile motion, profit-maximisation curves, and the trajectory of a thrown object. Printable grids and exemplar solutions make marking quick.