Exploring the properties of non-linear functions. SC

Students should be able to distinguish between a linear and quadratic graph, plot graphs of quadratic functions of the form y = x2 ± c and sketch a simple quadratic graph

Some students may incorrectly square negative values of x when plotting graphs of quadratic functions. Some may interpret a sketch is a very rough drawing. They need to appreciate that it should still be neat and identify key features, but will not be drawn to scale

Some pupils may think that the graph y = x2 + c is the graph of y = x2 translated horizontally.

 

Characteristics of quadratics

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Transforming simple quadratics









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Quadratic Graph Explorer.

This link could be used to explore quadratics generated by scientific formula such as equations of movement.

 

Interpreting Functions, Graphs and Tables A7

Quality AssuredCategory:MathematicsPublisher:Department for Education





normal">This activity looks at the relationship between graphical, algebraic and tabular representations of functions, including the nature of proportional, linear, quadratic and inverse functions.

normal"> 

normal">The staring points on page 1 outlines how students will already be familiar with making tabular representations of functions and drawing graphs, but they may not have considered the relations between different representations of functions.

normal">The resources describe how to start the lesson using card set A on page 5. Students are asked to consider which expression would give the largest value when n = 4. Students then match the formulae, words, graphs and tables in card sets B, C, D and E. You can use this resources to check prior knowledge before starting any unit of work that involves a range of graphs. If your mathematics department may have already used this resource you could use a couple of examples at the start of a lesson to make the link and check understanding. The examples used may depend on the students and your scientific objectives.

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Name="Body Text First Indent"/>
Name="Body Text First Indent 2"/>
Name="Note Heading"/>
Name="Body Text 2"/>
Name="Body Text 3"/>
Name="Body Text Indent 2"/>
Name="Body Text Indent 3"/>
Name="Block Text"/>
Name="Hyperlink"/>
Name="FollowedHyperlink"/>


Name="Document Map"/>
Name="Plain Text"/>
Name="E-mail Signature"/>
Name="HTML Top of Form"/>
Name="HTML Bottom of Form"/>
Name="Normal (Web)"/>
Name="HTML Acronym"/>
Name="HTML Address"/>
Name="HTML Cite"/>
Name="HTML Code"/>
Name="HTML Definition"/>
Name="HTML Keyboard"/>
Name="HTML Preformatted"/>
Name="HTML Sample"/>
Name="HTML Typewriter"/>
Name="HTML Variable"/>
Name="Normal Table"/>
Name="annotation subject"/>
Name="No List"/>
Name="Outline List 1"/>
Name="Outline List 2"/>
Name="Outline List 3"/>
Name="Table Simple 1"/>
Name="Table Simple 2"/>
Name="Table Simple 3"/>
Name="Table Classic 1"/>
Name="Table Classic 2"/>
Name="Table Classic 3"/>
Name="Table Classic 4"/>
Name="Table Colorful 1"/>
Name="Table Colorful 2"/>
Name="Table Colorful 3"/>
Name="Table Columns 1"/>
Name="Table Columns 2"/>
Name="Table Columns 3"/>
Name="Table Columns 4"/>
Name="Table Columns 5"/>
Name="Table Grid 1"/>
Name="Table Grid 2"/>
Name="Table Grid 3"/>
Name="Table Grid 4"/>
Name="Table Grid 5"/>
Name="Table Grid 6"/>
Name="Table Grid 7"/>
Name="Table Grid 8"/>
Name="Table List 1"/>
Name="Table List 2"/>
Name="Table List 3"/>
Name="Table List 4"/>
Name="Table List 5"/>
Name="Table List 6"/>
Name="Table List 7"/>
Name="Table List 8"/>
Name="Table 3D effects 1"/>
Name="Table 3D effects 2"/>
Name="Table 3D effects 3"/>
Name="Table Contemporary"/>
Name="Table Elegant"/>
Name="Table Professional"/>
Name="Table Subtle 1"/>
Name="Table Subtle 2"/>
Name="Table Web 1"/>
Name="Table Web 2"/>
Name="Table Web 3"/>
Name="Balloon Text"/>

Name="Table Theme"/>























Name="List Paragraph"/>

Name="Intense Quote"/>














































































Name="Subtle Emphasis"/>
Name="Intense Emphasis"/>
Name="Subtle Reference"/>
Name="Intense Reference"/>

UnhideWhenUsed="true" Name="Bibliography"/>
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>













Name="Grid Table 1 Light Accent 1"/>




Name="Grid Table 6 Colorful Accent 1"/>
Name="Grid Table 7 Colorful Accent 1"/>
Name="Grid Table 1 Light Accent 2"/>




Name="Grid Table 6 Colorful Accent 2"/>
Name="Grid Table 7 Colorful Accent 2"/>
Name="Grid Table 1 Light Accent 3"/>




Name="Grid Table 6 Colorful Accent 3"/>
Name="Grid Table 7 Colorful Accent 3"/>
Name="Grid Table 1 Light Accent 4"/>




Name="Grid Table 6 Colorful Accent 4"/>
Name="Grid Table 7 Colorful Accent 4"/>
Name="Grid Table 1 Light Accent 5"/>




Name="Grid Table 6 Colorful Accent 5"/>
Name="Grid Table 7 Colorful Accent 5"/>
Name="Grid Table 1 Light Accent 6"/>




Name="Grid Table 6 Colorful Accent 6"/>
Name="Grid Table 7 Colorful Accent 6"/>







Name="List Table 1 Light Accent 1"/>




Name="List Table 6 Colorful Accent 1"/>
Name="List Table 7 Colorful Accent 1"/>
Name="List Table 1 Light Accent 2"/>




Name="List Table 6 Colorful Accent 2"/>
Name="List Table 7 Colorful Accent 2"/>
Name="List Table 1 Light Accent 3"/>




Name="List Table 6 Colorful Accent 3"/>
Name="List Table 7 Colorful Accent 3"/>
Name="List Table 1 Light Accent 4"/>




Name="List Table 6 Colorful Accent 4"/>
Name="List Table 7 Colorful Accent 4"/>
Name="List Table 1 Light Accent 5"/>




Name="List Table 6 Colorful Accent 5"/>
Name="List Table 7 Colorful Accent 5"/>
Name="List Table 1 Light Accent 6"/>




Name="List Table 6 Colorful Accent 6"/>
Name="List Table 7 Colorful Accent 6"/>

/* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:8.0pt; mso-para-margin-left:0cm; line-height:107%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri",sans-serif; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-fareast-language:EN-US;}