Quadratic & Linear Function problem

Hello!

I have a more complex problem but for simplifications purposes I will explain it in simpler terms:

I have a function which I know its behaviour:

$\displaystyle y= x^2$ (IF x<a) OR $\displaystyle y=x$ (IF x>a).

Note that this is a single, continuum function. I have 2 problems in here:

1. I dont know how to write this down in an analytical formula. I want a general formula that gives me the expression of y and includes the conditions that if x<a or x>a;

2. What I want to plot is the crossover from the quadratic regime to the linear regime. That is, i want an analytical formula that gives me the expression of the crossover.

Could I have some help please? All tips are welcomed!

Many thanks