Is the equation y equals 3x2 plus 5 linear or nonlinear?

Answer 1

It is non-linear. Try graphing it, and see:

Calculate y, when x equals various values, such as -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, and 5.

Then, plot the points. Do they lie on a straight line? No, they lie on a bullet-shaped curve, called a parabola, if you have plotted the points correctly.

A quadratic function in x is one whose highest term is a multiple of x2, and the graph of any quadratic function has a shape like that described above; not a straight line.