# Functions & Graphs - Stage 4

This collection of resources that support the teaching of Equations and Formulae.

Here are some of the favourite activities selected by the NRICH team.

- Perpendicular Lines Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
- What’s that Graph? Can you work out which processes are represented by the graphs?
- Parabolic Patterns The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.
- Surprising Transformations I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

These are just a few of the activities on Functions and Graphs that you can find on the NRICH curriculum pages.

The activities below, taken from the STEM Learning website, complement the NRICH activities above.

### Graphs

**Graphs Pack two **has three relevant resources.

SMILE card 2249, **Gradients and Intercepts** (pdf pages 13-14) requires students to rearrange linear equations to make y the subject then sketch the graphs. The task has an example of this on the first page then questions lead students to consider the gradients of parallel and perpendicular lines.

SMILE card 2140, Quadratic Solutions (pdf pages 25-26) shows students how to solve quadratic equations using a graphical method. Then students use the drawn graphs to solve simultaneous quadratic and linear functions. Students are also required to consider when there are two, one or no real solutions.

SMILE card 2044, Matching Graphs (pdf pages 27-30) is a card sort where a set of functions need to be linked to corresponding graphs. The graphs involved are linear, quadratic and cubic.

### Quadratic Equations

This PowerPoint allows students to investigate the function f(x) =a(x+b)^{2}+c. They can alter the constants and view the position of the graph. With that knowledge students can then find the function for some given trajectories.

Slides 10 to15 deal with the position of the vertex and the roots of y=a(x+b)^{2}+c.

Slide 16 onwards return to the quadratic form y=ax^{2}+bx+c and progress to solving quadratic equations by factorising and using the standard formula.

### Graphs

**Graphical Representation of Quadratic Equations **has a set of eight graphs of quadratic functions and a set of eight quadratic equations. The task is to link each graph with the equation. The roots of the quadratic equations (some of which do not factorise) are the x intercepts of each corresponding graph.

The resource begins with teacher's notes.

### Graph Detectives

This resource contains an introductory Powerpoint, a list of functions and a set of posters of graphs. The task is to match each function with the appropriate graph. There is a mix of quadratic, cubic and reciprocal functions. The quadratic graphs may be found by transformations as those posters only show the graph of y=x^{2}. Graphs of other functions may need to be derived by plotting points.