Answer:

u(x) is the only quadratic function.

Step-by-step explanation:

We are given four algebraic functions in x and we have to find which one is a quadratic function.

Let us arrange those polynomials in descending powers of x.

i) u(x) = 3x^2-x-8

The highest degree is 2.  Hence this is quadratic function.

ii) v(x) = 8x^3+2x^2+9x

The highest degree is 3 and hence this is cubic

iii) y(x) = 3x^5+x^2+4

The highest degree is 5 and hence this cannot be quadratic

iv) z(x) = 2x^3+7x^2-3

The highest degree is 3 and hence this is cubic

Hence u(x) is the only quadratic function.