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5th May

5th May: Quadratic Functions

Learning Outcomes

Students studying at OL should be able to:

  • form quadratic equations given whole number roots
  • find first and second derivatives of quadratic functions
  • select and use suitable strategies (graphic,numeric, algebraic, mental) for finding solutions to equations of the form  f(x) = k with f(x) = ax2 + bx + c (and not necessarily factorisable) where a, b, c ∈ Q and interpret the results
  • select and use suitable strategies (graphic, numeric, algebraic, mental) for finding solutions to simultaneous linear equations one linear equation and one equation of order 2 with two unknowns (restricted to the case where either the coefficient of x or the coefficient of y is ± 1 in the linear equation) and interpret the results
  • graph functions of the form ax2 + bx + c where a, b, c ∈ Z , x ∈ R
Resources and Presentation
Explanatory Videos
GeoGebra Files
SEC Exam Questions

Quadratic patterns

https://www.scoilnet.ieuploads/resources/32764/32506.pptx Added: 28 Apr 2020 Contributor: PDST Resource type: Presentation

Teacher guide to a patterns approach to quadratic functions

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Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

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Language: English
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Quadratic Pattern Workbook

https://www.scoilnet.ieuploads/resources/29642/29378.pdf Added: 16 May 2019 Contributor: PDST Resource type: Other / Primary Source / Worksheet

A suite of quadratic patterns to help students get a deeper understanding of generalisations.

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Mathematics

Strand: 4. Algebra

Strand unit: 2. Solving Equations

Suggestions for use: To test students understanding of quadratic patterns by engaging with visual representations of patterns

Strand: 4. Algebra

Strand unit: 1. Expressions

Suggestions for use: To test students understanding of quadratic patterns by engaging with visual representations of patterns

Strand: 4. Algebra

Strand unit: 3. Inequalities

Suggestions for use: To test students understanding of quadratic patterns by engaging with visual representations of patterns

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Different Representations of Quadratic Functions

https://www.scoilnet.ieuploads/resources/29171/28907.pdf Added: 04 Mar 2019 Contributor: PDST Resource type:

Match the cards into 7 sets taking one card from each group. Discuss reasoning and be able to explain decisions.

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Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

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Graph Matching Activity on Quadratic Functions

https://www.scoilnet.ieuploads/resources/26434/26170.pdf Added: 24 Apr 2018 Contributor: PDST Resource type: Assessment

Student activity to assess their understanding of transformations of quadratic functions and their graphs. In this activity, students match quadratic functions given in different forms such as graph, vertex form, intercept form,.

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JC Mathematics
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Mathematics

Strand: 4. Algebra and Functions

Strand unit: 7. Functions

Suggestions for use: To assess student understanding of transformations of quadratic functions and their graphs

Key Skills: Communicating Working with Others Literacy Numeracy

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: To assess student understanding of transformations of quadratic functions and their graphs

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Shifting and Scaling Quadratic Functions - Student Activity

https://www.scoilnet.ieuploads/resources/26432/26168.pdf Added: 24 Apr 2018 Contributor: PDST Resource type: Worksheet

An activity investigating the affects of shifting and scaling on quadratic functions. Students are required to complete a table, plot points and draw the graph of different quadratic functions. They then investigate what effect changing a constant has on the graph.

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Mathematics

Strand: 4. Algebra and Functions

Strand unit: 7. Functions

Suggestions for use: help students understand the shape and properties of quadratic graphs

Key Skills: Communicating Working with Others Literacy Numeracy

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: help students understand the shape and properties of quadratic graphs

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Inequalities with Quadratics - HL

https://www.scoilnet.ieuploads/resources/28762/28498.pdf Added: 10 Nov 2018 Contributor: UCD MSC Resource type: Guide/notes

These UCD MSC notes demonstrate how students can solve inequalities with quadratics by finding where the quadratic cuts the x-axis. Students can do this by using the quadratic formula or by finding factors. The notes guide students by finding factors. This question is suitable for higher level students only.

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Strand: 4. Algebra

Strand unit: 3. Inequalities

Suggestions for use: Use the notes alongside the video tutorial. Students can use the video independently to increase their confidence in the topic of inequalities.

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One Linear, One Quadratic Equation - Part 2

https://www.scoilnet.ieuploads/resources/28743/28479.pdf Added: 05 Nov 2018 Contributor: UCD MSC Resource type: Guide/notes

Challenge your higher level mathematics students to this tricky question on finding the intersection point(s) of a linear and quadratic equation. The UCD MSC document provides teachers with the step-by-step workings and solution to the question.

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Strand: 4. Algebra

Strand unit: 2. Solving Equations

Suggestions for use: Use the notes alongside the video tutorial. Students can use the video independently to increase their confidence in the topic of solving equations.

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One Linear, One Quadratic Equation

https://www.scoilnet.ieuploads/resources/28740/28476.pdf Added: 05 Nov 2018 Contributor: UCD MSC Resource type: Guide/notes

Find the point(s) of intersection between a linear and a quadratic equation using the method of substitution. This UCD MSC document illustrates how students can solve the example question given.

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Mathematics

Strand: 4. Algebra

Strand unit: 2. Solving Equations

Suggestions for use: Use the notes alongside the video tutorial. Students can use the video independently to increase their confidence in the topic of solving equations.

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Forming Equations Given the Roots

https://www.scoilnet.ieuploads/resources/28738/28474.pdf Added: 05 Nov 2018 Contributor: UCD MSC Resource type: Guide/notes

Challenge students to form the quadratic equation by giving them the two roots. This UCD MSC document guides students through a step-by-step process in forming a quadratic equation from the roots x = -2 and x = 3. The example given is suitable for ordinary level students.

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Mathematics

Strand: 4. Algebra

Strand unit: 2. Solving Equations

Suggestions for use: Use the notes alongside the video tutorial. Students can use the video independently to increase their confidence in the topic of forming a quadratic equation. (Algebra -> Solving Equations)

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Introduction to Parabolas

https://youtu.be/BGz3pkoGPag Added: 27 Apr 2020 Contributor: PDST Resource type: Guide/notes

Khan Academy video providing an overview of a parabola

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Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: Guide notes

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Language: English
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Vertex Form of a Quadratic

http://www.showme.com/sh/?h=NyuZxIG Added: 04 May 2017 Contributor: Stephen Gammell Resource type: Guide/notes

How to complete a square to find a vertex

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Mathematics

Strand: 5. Functions

Strand unit: 2. Calculus

Suggestions for use: Low level, basic skills

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Derivative of a Quadratic Function

https://www.scoilnet.ie/pdst/maths/.../lc-functions/derivative/quadratic/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

Interactive Geogebra file to understand the form of the derivative of a quadratic function.

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Strand: 5. Functions

Strand unit: 2. Calculus

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Investigating the Change of the Change of a Pattern

https://www.scoilnet.ie/pdst/maths/...stigating-the-change-of-the-change/ Added: 26 Jun 2019 Contributor: PDST Resource type: Experiment / Guide/notes

Use this interactive file to learn what type of pattern is characterised by a constant change-of-change. Use this file in conjunction with the corresponding student activity. Drag the sliders to change the quadratic function. Observe the resulting changes in the graph and table. Can you spot a pattern? How would you identify a set of data as exhibiting quadratic behaviour?

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Mathematics

Strand: 4. Algebra and Functions

Strand unit: 1. Patterns and Relationships

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Solving a Linear and Quadratic Equation Simultaneously

https://www.scoilnet.ie/pdst/maths/student/lc/lc-algebra/simultaneous/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

GeoGebra interactive file and student activity sheet to learn how the intersection of the graphs of two functions relates to the solution to the equation f(x) = g(x)

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Strand: 4. Algebra

Strand unit: 2. Solving Equations

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2019 OL P1 Q7

https://www.scoilnet.ieuploads/resources/32756/32498.pdf Added: 27 Apr 2020 Contributor: PDST Resource type: Assessment

SEC Assessment Question

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Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: Assessment

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2017 OL P1 Q8

https://www.scoilnet.ieuploads/resources/32757/32499.pdf Added: 27 Apr 2020 Contributor: PDST Resource type: Assessment

SEC Exam Question

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Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: Assessment

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2016 OL P1 Q8

https://www.scoilnet.ieuploads/resources/32758/32500.pdf Added: 27 Apr 2020 Contributor: PDST Resource type: Assessment

SEC Exam Question

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Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: Assessment

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