State whether each equation in Exercises 25–30 represents a linear,

quadratic, or exponential function. Tell how you decided.

3x^2=5

*I believe this equation is a exponential function but, I'm not sure how to explain it.*

The determinant factor is the exponent.

If the variable is in the exponent, then it is exponential. For example,
4x+1=10

If the maximum value of the exponent is two, then the expression/equation is quadratic. For example:
x²+3x+1=0

If the maximum of the exponent is 1, or if exponents are absent (i.e. =1), it is linear. For example,
4x+5y=3

To determine whether an equation represents a linear, quadratic, or exponential function, we need to examine the highest power of the variable in the equation. In this case, the highest power of the variable is 2, as seen in the term "3x^2".

A linear function has the highest power of 1, such as "3x" or "2x + 5". An exponential function has the variable in the exponent, like "3^x" or "4^(2x)". A quadratic function has the highest power of 2, like "2x^2 + 3x + 7" or "x^2 - 9".

In the given equation, "3x^2 = 5", the highest power of x is 2, indicating that it is a quadratic function. The term "3x^2" is a quadratic term, and the constant term "5" does not introduce any exponential behavior.

Therefore, the equation "3x^2 = 5" represents a quadratic function.