Final Answer:
The value of f(-2) for the given function f(x) = 2
+ 3x + 1 is 3. It involves plugging the given value into the function and simplifying the expression according to mathematical rules.
Step-by-step explanation:
To find f(-2), substitute -2 for x in the function f(x) = 2
+ 3x + 1 :
![\[ f(-2) = 2(-2)^2 + 3(-2) + 1 \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/mpl0t9nvapbfmp35szuy7pfm9wd3uyg9qo.png)
Simplify the expression step by step:
f(-2) = 2(4) - 6 + 1
f(-2) = 8 - 6 + 1
f(-2) = 3
Therefore, f(-2) = 3
In this calculation, we substituted -2 for x in the given quadratic function and followed the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to evaluate the expression.
The result f(-2) = 3 represents the value of the quadratic function at x = -2 . This process is a fundamental concept in algebra, where we substitute specific values into functions to determine their corresponding outputs.