Evaluate the function [tex]f(x)=-2 x^2-3 x+5[/tex] for the input value -3
Answer (1)
To evaluate the function f ( x ) = − 2 x 2 − 3 x + 5 at x = − 3 :
Substitute x = − 3 into the function: f ( − 3 ) = − 2 ( − 3 ) 2 − 3 ( − 3 ) + 5 .
Simplify the expression: f ( − 3 ) = − 18 + 9 + 5 .
Calculate the final value: f ( − 3 ) = − 4 .
The value of the function at x = − 3 is − 4 .
Explanation
Understanding the problem We are asked to evaluate the function f ( x ) = − 2 x 2 − 3 x + 5 at x = − 3 . This means we need to substitute − 3 for x in the expression for f ( x ) and simplify.
Substitution Substitute x = − 3 into the function: f ( − 3 ) = − 2 ( − 3 ) 2 − 3 ( − 3 ) + 5
Simplification Now, we simplify the expression: f ( − 3 ) = − 2 ( 9 ) − ( − 9 ) + 5 f ( − 3 ) = − 18 + 9 + 5 f ( − 3 ) = − 9 + 5 f ( − 3 ) = − 4
Final Answer Therefore, the value of the function f ( x ) at x = − 3 is − 4 .
Examples
Evaluating functions is a fundamental concept in mathematics and has many real-world applications. For example, if you're tracking the height of a ball thrown into the air, you might use a function to model its trajectory. If you know the time elapsed since the ball was thrown, you can plug that time into the function to find 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. By evaluating the function at different production levels, you can make informed decisions about pricing and production volume.
