Find $f(-2)$ for the function $f(x)=3 x^2-2 x+7$.
Answer (1)
Substitute x = − 2 into the function f ( x ) = 3 x 2 − 2 x + 7 .
Calculate ( − 2 ) 2 = 4 .
Evaluate f ( − 2 ) = 3 ( 4 ) − 2 ( − 2 ) + 7 = 12 + 4 + 7 = 23 .
The final answer is 23 .
Explanation
Understanding the problem We are given the function f ( x ) = 3 x 2 − 2 x + 7 and asked to find the value of f ( − 2 ) . This means we need to substitute − 2 for x in the expression for f ( x ) .
Substituting x = -2 Now, let's substitute x = − 2 into the function: f ( − 2 ) = 3 ( − 2 ) 2 − 2 ( − 2 ) + 7
Simplifying the expression Next, we simplify the expression: f ( − 2 ) = 3 ( 4 ) + 4 + 7 f ( − 2 ) = 12 + 4 + 7 f ( − 2 ) = 23
Final Answer Therefore, the value of the function f ( x ) at x = − 2 is 23.
Examples
In physics, this type of polynomial function could describe the position of an object at a given time. For example, if f ( x ) represents the position of a car at time x , then finding f ( − 2 ) would tell us the position of the car 2 seconds in the past, assuming the model holds for negative time values. This is a direct application of evaluating a function at a specific point, which is a fundamental skill in many scientific and engineering fields.
