To identify the coefficients in the quadratic function, we need to compare it with the general form of a quadratic equation, which is given by:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
Let's analyze the given quadratic function:
[tex]\[ f(x) = 2x^2 - 5x \][/tex]
We will match the terms in this function to those in the general form.
1. The coefficient of [tex]\( x^2 \)[/tex] is [tex]\( a \)[/tex].
2. The coefficient of [tex]\( x \)[/tex] is [tex]\( b \)[/tex].
3. The constant term is [tex]\( c \)[/tex].
Looking at the function [tex]\( f(x) = 2x^2 - 5x \)[/tex]:
- The coefficient of [tex]\( x^2 \)[/tex] (which is [tex]\( a \)[/tex]) is 2.
- The coefficient of [tex]\( x \)[/tex] (which is [tex]\( b \)[/tex]) is -5.
- There is no constant term (which means [tex]\( c \)[/tex] is 0).
Thus, the coefficients are:
[tex]\[ a = 2 \][/tex]
[tex]\[ b = -5 \][/tex]
[tex]\[ c = 0 \][/tex]
So, the final answer is:
[tex]\[ a = 2, \quad b = -5, \quad c = 0 \][/tex]
