Thank you for the opportunity to help you with your question!
First off, think about variables and exponents. Consider the expression 5 * x. It is understood that the exponent on x is 1 (and, therefore, is not shown). Consider the expression 3 * x ^ 2: it is read out load as "3 times x squared". Because the exponent on x is 2, 3 * x^2 is a quadratic expression.
Next, let's look at equations. Now y = 3 * x^2 is a quadratic EQUATION (because of the equals sign). Now consider the equation x = 5 * y^2 + 3 *y + 7. It is still a quadratic equation, but the quadratic expression involves the variable y instead of the variable x. Also, the presence (or absence) of a linear term (like 3 * y) makes no difference as to whether the equation is quadratic or not. Is the equation 5x^2 - 3x + 3 = 0 a quadratic?
To check your answer, the following website might be helpful: https://www.mathsisfun.com/algebra/quadratic-equation.html
Please let me know if you need any clarification. I'm always happy to answer your questions.