To write the given quadratic function [tex]\( f(x) = 3x^2 - x + 1 \)[/tex] in standard form, we need to express it in the form:
[tex]\[ ax^2 + bx + c \][/tex]
Here are the steps:
1. Identify the coefficient of [tex]\( x^2 \)[/tex]:
The coefficient of [tex]\( x^2 \)[/tex] is the term in front of [tex]\( x^2 \)[/tex]. In this case, it is 3.
2. Identify the coefficient of [tex]\( x \)[/tex]:
The coefficient of [tex]\( x \)[/tex] is the term in front of [tex]\( x \)[/tex]. In this case, it is -1.
3. Identify the constant term:
The constant term is the term without any [tex]\( x \)[/tex]. In this case, it is 1.
So, the standard form of the given quadratic function is:
[tex]\[ 3x^2 - x + 1 \][/tex]
In summary:
- The coefficient [tex]\( a \)[/tex] is 3.
- The coefficient [tex]\( b \)[/tex] is -1.
- The constant term [tex]\( c \)[/tex] is 1.
Therefore, the quadratic function [tex]\( f(x) = 3x^2 - x + 1 \)[/tex] is already in standard form. The standard form is:
[tex]\[ f(x) = 3x^2 - x + 1 \][/tex]
where:
[tex]\[ a = 3 \][/tex]
[tex]\[ b = -1 \][/tex]
[tex]\[ c = 1 \][/tex]
