How to Evaluate a Quadratic Function: Step-by-Step Guide
Quick Answer
To evaluate a quadratic function like f(x) = x² - 5x + 7, substitute the value of x into the formula. For f(-4), the answer is 43, confirming your choice was correct!
Evaluating a quadratic function is an essential skill in algebra that can help you understand how these types of functions behave. Let’s take the function f(x) = x² - 5x + 7 as an example and evaluate it for x = -4.
**Step-by-Step Evaluation:**
1. **Substitution**: Start by substituting -4 into the function. This means replacing every x in the function with -4:
f(-4) = (-4)² - 5(-4) + 7
2. **Calculating (-4)²**: Remember, squaring a negative number means multiplying it by itself. So:
(-4)² = 16
3. **Calculating -5(-4)**: Here, you multiply -5 by -4. When you multiply two negatives, the result is positive:
-5 × -4 = 20
4. **Add the Results**: Now, combine all the parts:
16 (from (-4)²) + 20 (from -5(-4)) + 7.
So, 16 + 20 = 36, and then add 7:
36 + 7 = 43
Thus, f(-4) = 43, confirming your answer was correct!
**Tips for Future Substitutions**:
- Always use parentheses when substituting values to avoid confusion.
- Be cautious with signs, especially with negative numbers. A quick mental check can help you catch any mistakes.
**Real-World Applications**: Understanding quadratic functions isn’t just useful for homework; it has real-world applications. For example, quadratic functions can be used in physics to model projectile motion, in economics to determine profit maximization, and in various engineering fields to design structures.
With practice, evaluating functions like these will become second nature. Keep working through examples, and you'll become proficient in this essential algebra skill!
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