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Completing the Square - by InspectionIn this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
(Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square - maxima & maximaCompleting the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square - maxima & maximaCompleting the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
(Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the square - maxima and minimaThis is a workbook which describes how to complete the square for a quadratic expression. It goes on to show how the technique can be used
to find maximum or minimum values of a quadratic expression.
Completing the square - NumbasTwo questions on completing the square. The first asks you to express $x^2+ax+b$ in the form $(x+c)^2+d$ for suitable numbers $c$ and $d$. The second asks you to complete the square on the quadratic of the form $ax^2+bx+c$ and then find its roots.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Completing the square - NumbasTwo questions on completing the square. The first asks you to express $x^2+ax+b$ in the form $(x+c)^2+d$ for suitable numbers $c$ and $d$. The second asks you to complete the square on the quadratic of the form $ax^2+bx+c$ and then find its roots. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Completing the Square (to find MAX and MIN values) Part 1Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 2Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 3Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 4Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 5Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 6Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square 1In this iPOD video we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square 2In this iPOD video we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square 3In this iPOD video we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square 4In this iPOD video we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square 5In this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square 6In this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Complex arithmeticThis leaflet explains how complex numbers can added, subtracted, multiplied and divided. (Engineering Maths First Aid Kit 7.2)
Complex NumbersThis mobile phone video explains what is meant by a complex number, and how to find its real and imaginary parts.
Complex Numbers Arithmetic - Numbas6 questions on complex numbers, multiplication, inverse, division and modulus and finding the distance between complex numbers.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Complex Numbers Test 01 (DEWIS)Seven questions on complex numbers. Testing modulus, multiplication, division, Argand diagram, polar form, De Moivre's theorem. DEWIS resources have been made available under a Creative Commons licence by Rhys Gwynllyw & Karen Henderson, University of the West of England, Bristol.
Complex Roots of Polynomials - Numbas2 questions finding roots of real polynomials.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Complex roots of real polynomials - NumbasFinding roots of a cubic and the roots of a quartic by inspection. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Composition of functionsWe can build up complicated functions from simple functions by using the
process of composition, where the output of one function becomes the input of
another. It is also sometimes necessary to carry out the reverse process,
decomposing a complicated function into two or more simple functions.
This unit explains how.
Composition of functionsWe can build up complicated functions from simple functions by using the
process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to carry out the reverse process, decomposing a complicated function into two or more simple functions. This unit explains how. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
