Quadratic Function

Worksheets that build up the quadratic function step by step. Students first meet a new kind of growth through a fence problem and growing patterns, where the second differences are constant. Then they compare linear and quadratic growth in stories, tables, graphs and formulas, and draw the graph of f(x) = x². Next come the parabola’s shape and shifts, vertex form, zeros and the discriminant, quadratic inequalities, and modelling with maximum and minimum problems, projectiles and data. The last sheet is a group game with a check.

Quadratic Growth and the Graph

PDFA New Kind of Growththe fence problem, growing patterns, first and second differences · 3 pagesSEC
PDFLinear or Quadratic?differences, a card sort for groups, the height of a ball over time · 3 pagesSEC
PDFThe Function f(x) = x²table, graph, vertex, axis of symmetry, points on the graph · 2 pagesSEC
PDFThe Function f(x) = ax²width and direction of the parabola, matching formulas and graphs · 2 pagesSEC
PDFShifting the Parabolashifts up, down, left and right, why (x − 3)² moves right · 2 pagesSEC

The Vertex and Forms of the Function

PDFVertex Forma(x − p)² + q, vertex, axis of symmetry, formula from a graph · 2 pagesSEC
PDFCompleting the Squarecompleting the square step by step, algebra tiles · 2 pagesSEC
PDFThe Vertex from Standard Formfactoring out a, the vertex formula, largest and smallest values · 2 pagesSEC

Zeros and the Graph

PDFZeros of a Quadratic Functionzeros from the graph and by calculation, factored form · 2 pagesSEC
PDFHow Many Zeros?the discriminant, number of zeros, zeros and coefficients · 2 pagesSEC
PDFGraph from Formula, Formula from Graphdrawing in five steps, three forms of the formula · 2 pagesSEC
PDFBehaviour and Sign of a Functionincreasing, decreasing, smallest and largest value, sign · 2 pagesSEC

Quadratic Inequalities

PDFQuadratic Inequalities: Graphicallysolving with a sketch of the parabola, interval notation · 2 pagesSEC
PDFQuadratic Inequalities: All CasesD = 0 and D < 0, sign table, an application · 2 pagesSEC

Modelling

PDFModelling: Maximum and Minimumfences, revenue, the largest product, the modelling cycle · 2 pagesSEC
PDFModelling: Projectiles and Dataa ball thrown upwards, a model from measured data, a bridge arch · 2 pagesSEC

Review

PDFQuadratic Function: Practice and CheckFind the pair group game, a check, self-assessment · 2 pagesSEC

Students can also use the free Parabola app (tables and differences, three forms, sign and inequalities) and Algebra Tiles (completing the square) in the browser.