If [tex]$f(x)=-3(x-2)^2+6$[/tex], what is [tex]$f(0)$[/tex]?

Substitute x = 0 into the function f ( x ) = − 3 ( x − 2 ) 2 + 6 .
Calculate ( 0 − 2 ) 2 = ( − 2 ) 2 = 4 .
Multiply by -3: − 3 × 4 = − 12 .
Add 6: − 12 + 6 = − 6 .
The final answer is − 6 ​ .

Explanation

Understanding the problem We are given the function f ( x ) = − 3 ( x − 2 ) 2 + 6 and we want to find the value of f ( 0 ) . This means we need to substitute x = 0 into the expression for f ( x ) .

Substituting x=0 Substitute x = 0 into the function: f ( 0 ) = − 3 ( 0 − 2 ) 2 + 6

Simplifying the expression Now, we simplify the expression: f ( 0 ) = − 3 ( − 2 ) 2 + 6 f ( 0 ) = − 3 ( 4 ) + 6 f ( 0 ) = − 12 + 6 f ( 0 ) = − 6

Final Answer Therefore, the value of f ( 0 ) is − 6 .


Examples
Understanding function evaluation is crucial in many real-world applications. For example, in physics, if f ( x ) represents the height of a ball at time x , then f ( 0 ) would represent the initial height of the ball. Similarly, in economics, if f ( x ) represents the profit of a company when producing x items, then f ( 0 ) would represent the fixed costs of the company before producing any items. Evaluating functions at specific points helps us understand the state of a system at that particular input value.

Answered by GinnyAnswer | 2025-07-08

To find f ( 0 ) for the function f ( x ) = − 3 ( x − 2 ) 2 + 6 , we substitute x = 0 into the function, calculate, and find that f ( 0 ) = − 6 .
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Answered by Anonymous | 2025-08-24