To determine if the function [tex]\( y = 3x^2 + 2x - 3 \)[/tex] is linear, quadratic, or exponential, let's follow these steps:
1. Identify the degree of the polynomial:
The degree of a polynomial is determined by the highest power of the variable [tex]\( x \)[/tex] in the function. In the given function [tex]\( y = 3x^2 + 2x - 3 \)[/tex]:
- The term [tex]\( 3x^2 \)[/tex] has a degree of 2 because of the [tex]\( x^2 \)[/tex].
- The term [tex]\( 2x \)[/tex] has a degree of 1 because of the [tex]\( x \)[/tex].
- The constant term [tex]\(-3\)[/tex] has a degree of 0 because there is no [tex]\( x \)[/tex] involved.
The highest degree term is [tex]\( 3x^2 \)[/tex], which has a degree of 2.
2. Classify the function based on its degree:
- A linear function has a degree of 1 (e.g., [tex]\( y = mx + b \)[/tex]).
- A quadratic function has a degree of 2 (e.g., [tex]\( y = ax^2 + bx + c \)[/tex]).
- An exponential function has the variable as an exponent (e.g., [tex]\( y = a \cdot b^x \)[/tex]).
Given that the highest degree is 2, the function [tex]\( y = 3x^2 + 2x - 3 \)[/tex] is a quadratic function.
Therefore, the function [tex]\( y = 3x^2 + 2x - 3 \)[/tex] is quadratic.
