Quadratic Situations always have an x^2 in the equation. Their graphs have a turning point called a vertex. A common application of a quadratic is the height above the ground versus time of an object(projectile) that has been thrown. In a table, the second difference is the same.
Exponential Situations always MULTIPLY by the same amount each time. Common examples of exponential situations include percent increase or decrease (population growth, interest rates, etc.). Other words that will indicate multiplication (and thus exponential situations) are doubling, tripling, quadrupling, and increase by a factor of.