How to Evaluate Functions: Finding f(-3) for f(x) = x² + 10x + 6
Quick Answer
To find f(-3) for the function f(x) = x² + 10x + 6, substitute -3 for x. This gives you f(-3) = (-3)² + 10(-3) + 6 = -15.
Evaluating functions is an important skill in mathematics, and it involves substituting a specific value into the function. In this example, we will evaluate the function f(x) = x² + 10x + 6 at x = -3. Let's break it down step by step.
### Step 1: Substitute -3 into the function
The function we are working with is f(x) = x² + 10x + 6. To find f(-3), we need to replace every x in the function with -3:
f(-3) = (-3)² + 10(-3) + 6
### Step 2: Calculate (-3)²
First, we calculate (-3)². This means we are multiplying -3 by itself:
- (-3) × (-3) = 9.
### Step 3: Calculate 10(-3)
Next, we calculate 10 times -3:
- 10 × (-3) = -30.
### Step 4: Combine the results
Now we can combine the results from the previous steps:
- We have f(-3) = 9 (from step 2) + (-30) (from step 3) + 6.
### Step 5: Add it all together
Let's add these numbers together:
- Start with 9 + (-30) which equals -21.
- Now add 6: -21 + 6 = -15.
### Conclusion
Thus, the value of f(-3) is -15. This evaluation gives you insight into how the function behaves at that specific point. Understanding how to substitute values into functions is crucial not just for solving problems in algebra, but also in real-world applications such as physics, engineering, and economics, where functions often model relationships between quantities.
If you were to graph this function, you would see that it forms a parabola opening upwards, and evaluating points like f(-3) helps you understand its shape and behavior. Keep practicing evaluating functions, and soon you'll find it becomes second nature!
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