https://file.aiquickdraw.com/mathbot/file/1727278606643rzrmca4w.jpg

We are tasked with filling in the missing values for \( A \) and \( B \) in the given table, using the equation \( y = 2x^2 + x + 4 \).

We are provided with the following table of \( x \) and \( y \) values:

\[
\begin{array}{c|c|c|c|c|c}
x & -2 & -1 & 0 & 1 & 2 \\
\hline
y & A & 5 & 4 & B & 14 \\
\end{array}
\]

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.

Copy and complete the table of values for y = 2x^2 + x + 4. What numbers replace A and B?

Complete the table for y = 2x^2 + x + 4, replacing A and B using algebraic substitution. This step-by-step guide walks through the calculations for values of A and B, ideal for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation