Answer :
- Substitute $x=3$ into the function $f(x)=-5x^2-x+20$.
- Calculate $f(3) = -5(3)^2 - (3) + 20$.
- Simplify the expression: $f(3) = -5(9) - 3 + 20 = -45 - 3 + 20$.
- Evaluate to find the final answer: $f(3) = -28$.
### Explanation
1. Understanding the problem
We are given the function $f(x) = -5x^2 - x + 20$ and we want 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
Now, let's substitute $x = 3$ into the function:
$$f(3) = -5(3)^2 - (3) + 20$$
3. Squaring 3
Next, we need to simplify the expression. First, calculate $3^2$ which is $3 \times 3 = 9$. So we have:
$$f(3) = -5(9) - 3 + 20$$
4. Multiplying -5 by 9
Now, multiply $-5$ by $9$ which gives $-45$. So we have:
$$f(3) = -45 - 3 + 20$$
5. Subtracting 3 from -45
Next, we perform the addition and subtraction from left to right. First, $-45 - 3 = -48$. So we have:
$$f(3) = -48 + 20$$
6. Adding 20 to -48
Finally, $-48 + 20 = -28$. Therefore,
$$f(3) = -28$$
7. Final Answer
So, the value of the function $f(x)$ when $x = 3$ is $-28$.
### Examples
Understanding function evaluation is crucial in many real-world applications. For instance, in physics, if $f(x)$ represents the height of a projectile at time $x$, finding $f(3)$ tells us the height of the projectile at 3 seconds. Similarly, in economics, if $f(x)$ represents the cost of producing $x$ items, $f(3)$ gives the cost of producing 3 items. This concept is also used in computer science to determine the output of a function given a specific input.
- Calculate $f(3) = -5(3)^2 - (3) + 20$.
- Simplify the expression: $f(3) = -5(9) - 3 + 20 = -45 - 3 + 20$.
- Evaluate to find the final answer: $f(3) = -28$.
### Explanation
1. Understanding the problem
We are given the function $f(x) = -5x^2 - x + 20$ and we want 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
Now, let's substitute $x = 3$ into the function:
$$f(3) = -5(3)^2 - (3) + 20$$
3. Squaring 3
Next, we need to simplify the expression. First, calculate $3^2$ which is $3 \times 3 = 9$. So we have:
$$f(3) = -5(9) - 3 + 20$$
4. Multiplying -5 by 9
Now, multiply $-5$ by $9$ which gives $-45$. So we have:
$$f(3) = -45 - 3 + 20$$
5. Subtracting 3 from -45
Next, we perform the addition and subtraction from left to right. First, $-45 - 3 = -48$. So we have:
$$f(3) = -48 + 20$$
6. Adding 20 to -48
Finally, $-48 + 20 = -28$. Therefore,
$$f(3) = -28$$
7. Final Answer
So, the value of the function $f(x)$ when $x = 3$ is $-28$.
### Examples
Understanding function evaluation is crucial in many real-world applications. For instance, in physics, if $f(x)$ represents the height of a projectile at time $x$, finding $f(3)$ tells us the height of the projectile at 3 seconds. Similarly, in economics, if $f(x)$ represents the cost of producing $x$ items, $f(3)$ gives the cost of producing 3 items. This concept is also used in computer science to determine the output of a function given a specific input.
