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Answer :
- Substitute $x=3$ into the function $f(x)=-5 x^2-x+20$.
- Calculate $f(3) = -5(3)^2 - (3) + 20$.
- Simplify the expression: $f(3) = -45 - 3 + 20$.
- Find the final value: $f(3) = -28$, so the 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 $x = 3$. This means we need to substitute $3$ for $x$ in the expression for $f(x)$.
2. Substituting x=3
Now, let's substitute $x = 3$ into the function: $$f(3) = -5(3)^2 - (3) + 20$$
3. Simplifying the expression
Next, we simplify the expression using the order of operations (PEMDAS/BODMAS). First, we calculate $3^2 = 9$. Then, we multiply $-5$ by $9$ to get $-45$. So the expression becomes:$$f(3) = -45 - 3 + 20$$
4. Calculating the final value
Now, we perform the addition and subtraction from left to right:$$f(3) = -48 + 20 = -28$$Therefore, $f(3) = -28$.
### Examples
Understanding function evaluation is crucial in many real-world applications. For example, in physics, you might use a function to model the height of a projectile over time. Evaluating the function at a specific time tells you the height of the projectile at that moment. Similarly, in economics, a cost function can model the cost of producing a certain number of items. Evaluating the function tells you the cost for a specific production level. This concept is also used in computer graphics, where functions define the shapes and movements of objects.
- Calculate $f(3) = -5(3)^2 - (3) + 20$.
- Simplify the expression: $f(3) = -45 - 3 + 20$.
- Find the final value: $f(3) = -28$, so the 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 $x = 3$. This means we need to substitute $3$ for $x$ in the expression for $f(x)$.
2. Substituting x=3
Now, let's substitute $x = 3$ into the function: $$f(3) = -5(3)^2 - (3) + 20$$
3. Simplifying the expression
Next, we simplify the expression using the order of operations (PEMDAS/BODMAS). First, we calculate $3^2 = 9$. Then, we multiply $-5$ by $9$ to get $-45$. So the expression becomes:$$f(3) = -45 - 3 + 20$$
4. Calculating the final value
Now, we perform the addition and subtraction from left to right:$$f(3) = -48 + 20 = -28$$Therefore, $f(3) = -28$.
### Examples
Understanding function evaluation is crucial in many real-world applications. For example, in physics, you might use a function to model the height of a projectile over time. Evaluating the function at a specific time tells you the height of the projectile at that moment. Similarly, in economics, a cost function can model the cost of producing a certain number of items. Evaluating the function tells you the cost for a specific production level. This concept is also used in computer graphics, where functions define the shapes and movements of objects.
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