How does one identify a function as linear, quadratic, or neither? for example, f (x) = -x^2

for a function to be linear, it will be a straight line and use the equation y = mx + b (m = slope, b = y-intercept). for a function to be quadratic, it fill form a parabola (like patrick star's head), and use the equation Ax^2 + Bx + C = 0. the only neither i can currently think of is a sine wave, a line that goes up and down and looks like a sound wave.