Math Problem Statement
Copy and complete the table of values for y = 2x^2 + x + 4. What numbers replace A and B?
Solution
We are tasked with filling in the missing values for and in the given table, using the equation .
We are provided with the following table of and values:
x & -2 & -1 & 0 & 1 & 2 \\ \hline y & A & 5 & 4 & B & 14 \\ \end{array}$$ Let's calculate $$A$$ and $$B$$ by substituting the respective values of $$x$$ into the equation $$y = 2x^2 + x + 4$$. ### Step 1: Calculate $$A$$ when $$x = -2$$ Substitute $$x = -2$$ into the equation: $$y = 2(-2)^2 + (-2) + 4 = 2(4) - 2 + 4 = 8 - 2 + 4 = 10$$ Thus, $$A = 10$$. ### Step 2: Calculate $$B$$ when $$x = 1$$ Substitute $$x = 1$$ into the equation: $$y = 2(1)^2 + 1 + 4 = 2(1) + 1 + 4 = 2 + 1 + 4 = 7$$ Thus, $$B = 7$$. ### Final table: $$\begin{array}{c|c|c|c|c|c} x & -2 & -1 & 0 & 1 & 2 \\ \hline y & 10 & 5 & 4 & 7 & 14 \\ \end{array}$$ Would you like any further explanation or details? Here are 5 related questions to deepen your understanding: 1. How does the graph of $$y = 2x^2 + x + 4$$ look, and what are its key features? 2. What effect does changing the coefficient of $$x^2$$ in the equation have on the graph? 3. How can we find the vertex of the parabola represented by $$y = 2x^2 + x + 4$$? 4. How do the values of $$A$$ and $$B$$ relate to the symmetry of the parabola? 5. How would the equation change if the vertex of the parabola needed to be shifted? **Tip**: When working with quadratic functions, always substitute carefully and verify the signs during calculations to avoid common errors.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Substitution Method
Algebra
Formulas
y = 2x^2 + x + 4
Theorems
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Suitable Grade Level
Grades 7-9