Question

Is `y = x^2 + 1` an exponential function?

Answer 1

No, this is a quadratic function. Graphically it will give you a Parabola:
graph{x^2+1 [-10, 10, -5, 5]}
To have an exponential, the variable `x` must appear as an exponent of some number `a`: for example `a^x`.
Have a look: