### Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

### How Many Solutions?

Find all the solutions to the this equation.

Try to decide how the graph of $y=x^2$ is transformed to give the graphs of $y=ax^2$, $y=(x+b)^2$ and $y=x^2+c$ by experimenting with some small integer values of $a$, $b$ and $c$, both positive and negative.