# Functions and Graphs - Stage 4

### Doesn't Add Up

##### Age 14 to 16 Challenge Level:

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

### Parabolic Patterns

##### Age 14 to 18 Challenge Level:

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

### Exploring Cubic Functions

##### Age 14 to 18 Challenge Level:

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

### Steady Free Fall

##### Age 14 to 16 Challenge Level:

Can you adjust the curve so the bead drops with near constant vertical velocity?

### Perpendicular Lines

##### Age 14 to 16 Challenge Level:

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

### Negatively Triangular

##### Age 14 to 16 Challenge Level:

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

### At Right Angles

##### Age 14 to 16 Challenge Level:

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

### Tangled Trig Graphs

##### Age 16 to 18 Challenge Level:

Can you work out the equations of the trig graphs I used to make my pattern?

### Back Fitter

##### Age 14 to 16 Challenge Level:

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

### Surprising Transformations

##### Age 14 to 16 Challenge Level:

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?

### What's That Graph?

##### Age 14 to 16 Challenge Level:

Can you work out which processes are represented by the graphs?

### Functions and Graphs - Short Problems

##### Age 11 to 16

A collection of short problems on straight line graphs.

### Inside a Parabola

##### Age 14 to 16 Short Challenge Level:

A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.

### Triangular Slope

##### Age 14 to 16 Short Challenge Level:

Can you find the gradients of the lines that form a triangle?

### Graph Triangles

##### Age 14 to 16 Short Challenge Level:

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

### Closer to Home

##### Age 14 to 16 Short Challenge Level:

Which of these lines comes closer to the origin?