Answer
No, the function $f(x)=1.5x^2$ is not an exponential function.
Work Step by Step
Given $f(x) = 1.5x^2$ we can see that it is not of the form $f(x) = b^x$ ($x$ is not an exponent).
The function $f(x)=1.5x^2$ is a quadratic function, the variable $x$ is raised to the power of 2.