A quadratic equation is an equation with exponents and x's, for example 3x^2+4x+3 is a quadratic. and quadratics usually have two points it can cross the x axis. though that doesn't mean it always crosses twice. some quadratic equations can cross more then twice and some don't at all.
linear equations are simple. they always show a straight line on a graph.
And exponential are kind like quadratics, exponential always have an exponent but don't have multiple x intercepts. exponentials are equations like the equation for compound interest rates (Initial Account Balance * (Interest Rates) ^ Time) it is exponentially growing using exponents.
