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These are the Transum resources related to the statement: "Work with quadratic functions and their graphs. The discriminant of a quadratic function, including the conditions for real and repeated roots. Completing the square. Solution of quadratic equations including solving quadratic equations in a function of the unknown.".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Completing the Square Practise this technique for use in solving quadratic equations and analysing graphs.
- Factorising Quadratics An exercise about factorising quadratics presented one question at a time suitable for a whole class activity.
- Graph Equation Pairs Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function.
- Graph Match Match the equations with the images of the corresponding graphs. A drag-and-drop activity.
- Graph Patterns Find the equations which will produce the given patterns of graphs.
- Graph Plotter An online tool to draw, display and investigate graphs of many different kinds.
- Human Graphs Students should be encouraged to stand up and make the shapes of the graphs with their arms.
- New Way to Solve Quadratics A computationally-efficient, natural, and easy-to-remember algorithm for solving general quadratic equations.
- Old Equations Solve these linear equations that appeared in a book called A Graduated Series of Exercises in Elementary Algebra by Rev George Farncomb Wright published in 1857.
- Plotting Graphs Complete a table of values then plot the corresponding points to create a graph.
- Using Graphs Use the graphs provided to solve both simultaneous and quadratic equations.
- Yes No Questions A game to determine the mathematical item by asking questions that can only be answered yes or no.

Here are some exam-style questions on this statement:

- "
*Match the equation with the letter of its graph*" ... more - "
*The graph of y = f(x) is drawn accurately on the grid.*" ... more - "
*(a) By completing the square, solve \(x^2+8x+13=0\) giving your answer to three significant figures.*" ... more - "
*The graph of the following equation is drawn and then reflected in the x-axis*" ... more - "
*The diagram below is a sketch of a curve, a parabola, which is not drawn to scale.*" ... more - "
*(a) Find the interval for which \(x^2 - 9x + 18 \le 0\)*" ... more - "
*(a) Write \(2x^2+8x+27\) in the form \(a(x+b)^2+c\) where \(a\), \(b\), and \(c\) are integers, by 'completing the square'*" ... more - "
*A function is defined as \(f(x) = 2{(x - 3)^2} - 5\) .*" ... more - "
*Let \(f(x)=5x^2-20x+k\). The equation \(f(x)=0\) has two equal roots.*" ... more

Click on a topic below for suggested lesson starters, resources and activities from Transum.

- Algebra Pupils begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or many operations. They use brackets, indices and other constructs to apply algebra to real word problems. This leads to using algebra as an invaluable tool for solving problems, modelling situations and investigating ideas. If this topic were split into four sub topics they might be: Creating and simplifying expressions; Expanding and factorising expressions; Substituting and using formulae; Solving equations and real life problems; This is a powerful topic and has strong links to other branches of mathematics such as number, geometry and statistics. See also "Number Patterns", "Negative Numbers" and "Simultaneous Equations".
- Graphs This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts. A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops. Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.

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