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### Parabolic Patterns

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.

### More 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.

# Electric Kettle

##### Stage: 4 Challenge Level:

The diagram shows a simple circuit: the cell provides energy, V volts, which causes a current, I amps, to flow around the circuit. There is also a resistance, R ohms.

This circuit provides a simple model for what happens in an electric kettle: a resistance converts electrical energy into heat energy by impeding the flow of electrons around the circuit.

The table shows data collected from a circuit like this.

 Resistance (ohms) Temperature (degrees Celsius) 5 44.9 6 50 7 55.1 8 59.9 9 65 10 70.1

• Draw a graph of this data, with the resistance on the horizontal axis, putting a straight line through the points.
• Find the gradient of the line.
• Find the equation of the line.

Once you have found the equation, discuss these questions:

• What resistance would you need to heat water to 100 C°?
• What would the temperature be if the resistance was zero?
• Do you think that in practice, any circuit can have zero resistance?