Is x^2+13x-4=0 a quatratic function? why?

Yes it is a quadratic function. A quadratic function contains the term x^2 and x^2 has the highest exponent in the whole function of a quadratic function. What I mean by this is for example x^3 + x^2 + 2x + 3 is not a quadratic. It includes x^2 but x^3 has the largest exponent. That makes that equation a cubic. Just for more info the largest exponent is referred to as the degree of the function so the degree of a quadratic function is always 2. Hope this helps!