If [tex]$f(x)=-4 x^2+7 x-15$[/tex], what is [tex]$f(0)$[/tex]?
Answer (1)
Substitute x = 0 into the function f ( x ) = − 4 x 2 + 7 x − 15 .
Calculate f ( 0 ) = − 4 ( 0 ) 2 + 7 ( 0 ) − 15 .
Simplify the expression to get f ( 0 ) = 0 + 0 − 15 .
The final answer is − 15 .
Explanation
Understanding the problem We are given the function f ( x ) = − 4 x 2 + 7 x − 15 and we want to find the value of the function when x = 0 . This is written as f ( 0 ) .
Substituting x=0 To find f ( 0 ) , we substitute x = 0 into the expression for f ( x ) : f ( 0 ) = − 4 ( 0 ) 2 + 7 ( 0 ) − 15
Simplifying the expression Now we simplify the expression: f ( 0 ) = − 4 ( 0 ) + 7 ( 0 ) − 15 f ( 0 ) = 0 + 0 − 15 f ( 0 ) = − 15
Final Answer Therefore, f ( 0 ) = − 15 .
Examples
In physics, if you have a function that describes the height of a ball thrown in the air as h ( t ) = − 4.9 t 2 + 20 t + 2 , where t is time in seconds, finding h ( 0 ) would tell you the initial height of the ball at the moment it was thrown (at t = 0 ). This is a direct application of evaluating a function at a specific point, providing a real-world interpretation of the function's value at that point.
