state whether each relation y=f(x) describes a quadratic function or not
yes
no
maybe
y = 3x + 3
To determine whether a relation y = f(x) describes a quadratic function, we need to analyze its equation and check whether the highest power of the variable x is 2.
A quadratic function has the form y = ax^2 + bx + c, where a, b, and c are constants, and a ≠ 0.
Here are the steps to determine whether a relation represents a quadratic function:
1. Examine the equation to verify if the variable x is raised to the power of 2.
- If x is raised only to the power of 2, for example, y = 3x^2, it is a quadratic function.
- If x is raised to a power higher than 2 or if it is raised to a fractional or negative power, it does not represent a quadratic function.
2. Check if there are any terms multiplied by x (without any exponents).
- If an x term is present without any exponent other than 1 (e.g., y = 2x), it is not a quadratic function.
- If x is multiplied by a constant in addition to the quadratic term (e.g., y = 2x^2 + 3x), it is still considered a quadratic function.
3. Look for any constants (terms without x).
- Quadratic functions may contain constant terms (e.g., y = x^2 + 5), and their presence does not affect the classification.
Based on these steps, analyze each of the relations y = f(x) to determine if it describes a quadratic function.