Answer :
To determine whether a polynomial function with a degree of 2 is called a Quadratic Function, let's analyze the statement step-by-step.
1. Definition of a Polynomial:
A polynomial is an algebraic expression that consists of variables and coefficients, constructed using operations of addition, subtraction, multiplication, and non-negative integer exponents.
2. Degree of a Polynomial:
The degree of a polynomial is the highest power of the variable in the polynomial. For example:
- [tex]\( f(x) = 3x^2 + 2x + 1 \)[/tex] is a polynomial of degree 2 because the highest exponent of [tex]\( x \)[/tex] is 2.
- [tex]\( g(x) = 5x^3 - 4x^2 + x - 2 \)[/tex] is a polynomial of degree 3 because the highest exponent of [tex]\( x \)[/tex] is 3.
3. Quadratic Function:
A quadratic function is a specific type of polynomial function where the degree is exactly 2. It has the general form:
[tex]\[ f(x) = ax^2 + bx + c \][/tex]
where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants, and [tex]\( a \neq 0 \)[/tex]. The term [tex]\( a \cdot x^2 \)[/tex] is what gives the function its quadratic nature.
Given this information, a polynomial function with a degree of 2 is appropriately known as a Quadratic Function.
Therefore, the statement:
"A polynomial function with a degree of 2 is called a Quadratic Function"
is True.
1. Definition of a Polynomial:
A polynomial is an algebraic expression that consists of variables and coefficients, constructed using operations of addition, subtraction, multiplication, and non-negative integer exponents.
2. Degree of a Polynomial:
The degree of a polynomial is the highest power of the variable in the polynomial. For example:
- [tex]\( f(x) = 3x^2 + 2x + 1 \)[/tex] is a polynomial of degree 2 because the highest exponent of [tex]\( x \)[/tex] is 2.
- [tex]\( g(x) = 5x^3 - 4x^2 + x - 2 \)[/tex] is a polynomial of degree 3 because the highest exponent of [tex]\( x \)[/tex] is 3.
3. Quadratic Function:
A quadratic function is a specific type of polynomial function where the degree is exactly 2. It has the general form:
[tex]\[ f(x) = ax^2 + bx + c \][/tex]
where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants, and [tex]\( a \neq 0 \)[/tex]. The term [tex]\( a \cdot x^2 \)[/tex] is what gives the function its quadratic nature.
Given this information, a polynomial function with a degree of 2 is appropriately known as a Quadratic Function.
Therefore, the statement:
"A polynomial function with a degree of 2 is called a Quadratic Function"
is True.
