Evaluate The Function G ( X ) = − 2 X 2 + 3 X − 5 G(x) = -2x^2 + 3x - 5 G ( X ) = − 2 X 2 + 3 X − 5 For The Input Values − 2 , 0 -2, 0 − 2 , 0 , And 3 3 3 .${ \begin{align*} g(-2) & = -2(-2)^2 + 3(-2) - 5 \ g(-2) & = -2(4) - 6 - 5 \ g(-2) & = \square \ \end{align*} }$[ g(0) =
Introduction
In mathematics, functions are used to describe the relationship between variables. Evaluating a function at a given input value is a crucial step in understanding its behavior and properties. In this article, we will evaluate the function g(x) = -2x^2 + 3x - 5 for the input values -2, 0, and 3.
Evaluating g(-2)
To evaluate g(-2), we need to substitute x = -2 into the function g(x) = -2x^2 + 3x - 5.
g(-2) = -2(-2)^2 + 3(-2) - 5
Expanding the squared term, we get:
g(-2) = -2(4) - 6 - 5
Simplifying the expression, we get:
g(-2) = -8 - 6 - 5
Combining like terms, we get:
g(-2) = -19
Therefore, g(-2) = -19.
Evaluating g(0)
To evaluate g(0), we need to substitute x = 0 into the function g(x) = -2x^2 + 3x - 5.
g(0) = -2(0)^2 + 3(0) - 5
Since any number raised to the power of 0 is 1, and any number multiplied by 0 is 0, we get:
g(0) = -2(1) + 0 - 5
Simplifying the expression, we get:
g(0) = -2 - 5
Combining like terms, we get:
g(0) = -7
Therefore, g(0) = -7.
Evaluating g(3)
To evaluate g(3), we need to substitute x = 3 into the function g(x) = -2x^2 + 3x - 5.
g(3) = -2(3)^2 + 3(3) - 5
Expanding the squared term, we get:
g(3) = -2(9) + 9 - 5
Simplifying the expression, we get:
g(3) = -18 + 9 - 5
Combining like terms, we get:
g(3) = -14
Therefore, g(3) = -14.
Conclusion
In this article, we evaluated the function g(x) = -2x^2 + 3x - 5 for the input values -2, 0, and 3. We found that g(-2) = -19, g(0) = -7, and g(3) = -14. These results demonstrate the importance of evaluating functions at specific input values to understand their behavior and properties.
Discussion
Evaluating functions is a fundamental concept in mathematics, and it has numerous applications in various fields, including physics, engineering, and economics. By understanding how functions behave at specific input values, we can make informed decisions and predictions about real-world phenomena.
Future Work
In future work, we can explore other functions and evaluate them at different input values. We can also investigate the properties of functions, such as their domain, range, and continuity. Additionally, we can apply function evaluation to solve real-world problems and make predictions about complex systems.
References
- [1] "Functions" by Khan Academy
- [2] "Evaluating Functions" by Mathway
- [3] "Functions and Relations" by Wolfram MathWorld
Appendix
The following is a list of formulas and equations used in this article:
- g(x) = -2x^2 + 3x - 5
- g(-2) = -2(-2)^2 + 3(-2) - 5
- g(0) = -2(0)^2 + 3(0) - 5
- g(3) = -2(3)^2 + 3(3) - 5
Introduction
In our previous article, we evaluated the function g(x) = -2x^2 + 3x - 5 for the input values -2, 0, and 3. In this article, we will answer some frequently asked questions (FAQs) about the function g(x) and its evaluation.
Q: What is the domain of the function g(x) = -2x^2 + 3x - 5?
A: The domain of a function is the set of all possible input values for which the function is defined. In this case, the function g(x) = -2x^2 + 3x - 5 is defined for all real numbers, so the domain is all real numbers, denoted as (-∞, ∞).
Q: What is the range of the function g(x) = -2x^2 + 3x - 5?
A: The range of a function is the set of all possible output values for which the function is defined. In this case, the function g(x) = -2x^2 + 3x - 5 is a quadratic function, and its range is all real numbers, denoted as (-∞, ∞).
Q: How do I evaluate the function g(x) = -2x^2 + 3x - 5 at a specific input value?
A: To evaluate the function g(x) = -2x^2 + 3x - 5 at a specific input value, simply substitute the input value into the function and simplify the expression. For example, to evaluate g(2), we would substitute x = 2 into the function and get:
g(2) = -2(2)^2 + 3(2) - 5 g(2) = -2(4) + 6 - 5 g(2) = -8 + 6 - 5 g(2) = -7
Q: Can I use a calculator to evaluate the function g(x) = -2x^2 + 3x - 5?
A: Yes, you can use a calculator to evaluate the function g(x) = -2x^2 + 3x - 5. Simply enter the input value and the function into the calculator, and it will give you the output value.
Q: How do I graph the function g(x) = -2x^2 + 3x - 5?
A: To graph the function g(x) = -2x^2 + 3x - 5, you can use a graphing calculator or a computer program such as Desmos. Simply enter the function into the graphing tool, and it will display the graph of the function.
Q: Can I use the function g(x) = -2x^2 + 3x - 5 to model real-world phenomena?
A: Yes, you can use the function g(x) = -2x^2 + 3x - 5 to model real-world phenomena. For example, you can use this function to model the motion of an object under the influence of gravity or to model the growth of a population.
Conclusion
In this article, we answered some frequently asked questions about the function g(x) = -2x^2 + 3x - 5 and its evaluation. We hope that this article has been helpful in understanding the function and its properties.
Discussion
Evaluating functions is a fundamental concept in mathematics, and it has numerous applications in various fields, including physics, engineering, and economics. By understanding how functions behave at specific input values, we can make informed decisions and predictions about real-world phenomena.
Future Work
In future work, we can explore other functions and evaluate them at different input values. We can also investigate the properties of functions, such as their domain, range, and continuity. Additionally, we can apply function evaluation to solve real-world problems and make predictions about complex systems.
References
- [1] "Functions" by Khan Academy
- [2] "Evaluating Functions" by Mathway
- [3] "Functions and Relations" by Wolfram MathWorld
Appendix
The following is a list of formulas and equations used in this article:
- g(x) = -2x^2 + 3x - 5
- g(-2) = -2(-2)^2 + 3(-2) - 5
- g(0) = -2(0)^2 + 3(0) - 5
- g(3) = -2(3)^2 + 3(3) - 5
Note: The formulas and equations are listed in the appendix for reference purposes only.