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 f ( − 3 ) = − 2 ( − 3 ) 2 − 5 ( − 3 ) + 4 .
Simplify the expression: f ( − 3 ) = − 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
Imagine you are tracking the trajectory of a ball thrown in the air, and its height is described by the function f ( t ) = − 2 t 2 − 5 t + 4 , where t is the time in seconds. Finding f ( − 3 ) might not have a direct physical meaning in this context since time cannot be negative, but understanding how to evaluate such functions is crucial for analyzing the ball's motion within realistic time frames. Evaluating functions at specific points helps in predicting outcomes and understanding the behavior of various phenomena in physics, engineering, and other fields. For example, we can determine the height of the ball at different times by substituting those times into the function.
