Answer :
* The problem asks to find $f(3)$ for the function $f(x) = -5x^2 - x + 20$.
* Substitute $x = 3$ into the function: $f(3) = -5(3)^2 - (3) + 20$.
* Simplify the expression: $f(3) = -5(9) - 3 + 20 = -45 - 3 + 20 = -48 + 20 = -28$.
* The final answer is $\boxed{{-28}}$.
### Explanation
1. Understanding the problem
We are given the function $f(x) = -5x^2 - x + 20$ and asked to find the value of the function when $x = 3$, which is denoted as $f(3)$. This means we need to substitute $x = 3$ into the expression for $f(x)$ and simplify.
2. Substituting x = 3
To find $f(3)$, we replace every instance of $x$ in the function's expression with the number 3. So we have:
$$f(3) = -5(3)^2 - (3) + 20$$
3. Evaluating the exponent
Now, we simplify the expression using the order of operations (PEMDAS/BODMAS). First, we evaluate the exponent:
$$f(3) = -5(9) - 3 + 20$$
4. Performing the multiplication
Next, we perform the multiplication:
$$f(3) = -45 - 3 + 20$$
5. Performing addition and subtraction
Now, we perform the addition and subtraction from left to right:
$$f(3) = -48 + 20$$
6. Final Calculation
Finally, we have:
$$f(3) = -28$$
7. Conclusion
Therefore, the value of the function $f(x)$ at $x=3$ is $-28$.
### Examples
Understanding function evaluation is crucial in many real-world applications. For instance, in physics, you might use a function to model the height of a projectile over time. Evaluating the function at a specific time (like x=3 seconds) tells you the height of the projectile at that moment. Similarly, in economics, a cost function could tell you the cost of producing a certain number of items. Evaluating the function helps you determine the cost for a specific production level.
* Substitute $x = 3$ into the function: $f(3) = -5(3)^2 - (3) + 20$.
* Simplify the expression: $f(3) = -5(9) - 3 + 20 = -45 - 3 + 20 = -48 + 20 = -28$.
* The final answer is $\boxed{{-28}}$.
### Explanation
1. Understanding the problem
We are given the function $f(x) = -5x^2 - x + 20$ and asked to find the value of the function when $x = 3$, which is denoted as $f(3)$. This means we need to substitute $x = 3$ into the expression for $f(x)$ and simplify.
2. Substituting x = 3
To find $f(3)$, we replace every instance of $x$ in the function's expression with the number 3. So we have:
$$f(3) = -5(3)^2 - (3) + 20$$
3. Evaluating the exponent
Now, we simplify the expression using the order of operations (PEMDAS/BODMAS). First, we evaluate the exponent:
$$f(3) = -5(9) - 3 + 20$$
4. Performing the multiplication
Next, we perform the multiplication:
$$f(3) = -45 - 3 + 20$$
5. Performing addition and subtraction
Now, we perform the addition and subtraction from left to right:
$$f(3) = -48 + 20$$
6. Final Calculation
Finally, we have:
$$f(3) = -28$$
7. Conclusion
Therefore, the value of the function $f(x)$ at $x=3$ is $-28$.
### Examples
Understanding function evaluation is crucial in many real-world applications. For instance, in physics, you might use a function to model the height of a projectile over time. Evaluating the function at a specific time (like x=3 seconds) tells you the height of the projectile at that moment. Similarly, in economics, a cost function could tell you the cost of producing a certain number of items. Evaluating the function helps you determine the cost for a specific production level.
