Math Problem Statement
Form a quadratic function f(x) that has three values of x and f(x) corresponding to -1, 0, and 1 from the given table. Which equation correctly represents it?
Solution
The problem in the image involves identifying the quadratic function based on a given table of values. The table provides the following points:
x & f(x) \\ \hline -1 & 33 \\ 0 & 18 \\ 1 & 33 \\ \end{array}$$ The problem asks which equation best represents this quadratic function $$f(x)$$ from the provided options: 1. $$f(x) = 10x^2 + 8x + 18$$ 2. $$f(x) = 15x^2 + 3x + 18$$ 3. $$f(x) = -15x^2 + 18$$ 4. $$f(x) = 10x^2 + 18$$ ### Step 1: Recognize the form of the quadratic equation. A quadratic function generally has the form $$f(x) = ax^2 + bx + c$$. ### Step 2: Plug in the values of $$x$$ and $$f(x)$$ from the table into each equation to see which one fits. 1. **Option 1**: $$f(x) = 10x^2 + 8x + 18$$ - For $$x = -1$$: $$f(-1) = 10(-1)^2 + 8(-1) + 18 = 10 - 8 + 18 = 20$$ (not 33). - This does not match, so this is not the correct equation. 2. **Option 2**: $$f(x) = 15x^2 + 3x + 18$$ - For $$x = -1$$: $$f(-1) = 15(-1)^2 + 3(-1) + 18 = 15 - 3 + 18 = 30$$ (not 33). - This does not match, so this is not the correct equation. 3. **Option 3**: $$f(x) = -15x^2 + 18$$ - For $$x = -1$$: $$f(-1) = -15(-1)^2 + 18 = -15 + 18 = 3$$ (not 33). - This does not match, so this is not the correct equation. 4. **Option 4**: $$f(x) = 10x^2 + 18$$ - For $$x = -1$$: $$f(-1) = 10(-1)^2 + 18 = 10 + 18 = 28$$ (not 33). - This does not match either. Since none of the options directly match with the given values, there seems to be a mistake in the problem's setup or the provided options. It’s possible that either the given options need reevaluation or additional information might be required. Would you like to go through this in more detail or ask any additional questions? Here are some related questions that might help: 1. How can you derive a quadratic function from three given points? 2. How do you check if a function is quadratic? 3. What are the properties of quadratic functions? 4. How do you determine the vertex of a quadratic function from its equation? 5. What methods can be used to factorize quadratic equations? **Tip:** When testing function values, always ensure to substitute carefully and consider each coefficient's role in the quadratic function.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Substitution Method
Formulas
Quadratic function f(x) = ax^2 + bx + c
Theorems
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Suitable Grade Level
Grades 8-10
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