What is $f(-3)$ for the function $f(a)=-2 a^2-5 a+4$?
Answer (1)
Substitute a = − 3 into the function f ( a ) = − 2 a 2 − 5 a + 4 .
Calculate ( − 3 ) 2 = 9 .
Simplify the expression: f ( − 3 ) = − 2 ( 9 ) − 5 ( − 3 ) + 4 = − 18 + 15 + 4 = 1 .
The final answer is 1 .
Explanation
Understanding the problem We are given the function f ( a ) = − 2 a 2 − 5 a + 4 and we want to find the value of f ( − 3 ) . This means we need to substitute − 3 for a in the expression for f ( a ) .
Substituting the value Now, let's substitute a = − 3 into the function: f ( − 3 ) = − 2 ( − 3 ) 2 − 5 ( − 3 ) + 4
Simplifying the expression Next, we simplify the expression: f ( − 3 ) = − 2 ( 9 ) + 15 + 4 f ( − 3 ) = − 18 + 15 + 4 f ( − 3 ) = − 3 + 4 f ( − 3 ) = 1
Final Answer Therefore, the value of the function f ( a ) when a = − 3 is 1.
Examples
Evaluating functions is a fundamental concept in mathematics and has many real-world applications. For instance, if you're tracking the trajectory of a ball thrown in the air, the function might describe the height of the ball at a given time. By evaluating the function at a specific time, you can determine the ball's height at that moment. Similarly, in business, a cost function can tell you the total cost of producing a certain number of items. Evaluating this function helps in making informed decisions about production levels and pricing strategies.
