To complete the table of values for the quadratic function \( y = x^2 + 4x - 3 \), let's calculate the values of \( y \) for each given \( x \) value.
Here is the table that we need to complete:
[tex]\[
\begin{array}{c||c|c|c|c|c}
x & -3 & -2 & -1 & 0 & 1 \\
\hline
y & A & -7 & -6 & B & C \\
\end{array}
\][/tex]
Given:
1. When \( x = -2 \), \( y = -7 \)
2. When \( x = -1 \), \( y = -6 \)
We need to find the values that replace \( A \), \( B \), and \( C \).
Let's calculate each required value step-by-step.
1. For \( x = -3 \):
[tex]\[
y = (-3)^2 + 4(-3) - 3 = 9 - 12 - 3 = -6
\][/tex]
So, \( A = -6 \).
2. For \( x = 0 \):
[tex]\[
y = (0)^2 + 4(0) - 3 = 0 + 0 - 3 = -3
\][/tex]
So, \( B = -3 \).
3. For \( x = 1 \):
[tex]\[
y = (1)^2 + 4(1) - 3 = 1 + 4 - 3 = 2
\][/tex]
So, \( C = 2 \).
Now, we can complete the table:
[tex]\[
\begin{array}{c||c|c|c|c|c}
x & -3 & -2 & -1 & 0 & 1 \\
\hline
y & -6 & -7 & -6 & -3 & 2 \\
\end{array}
\][/tex]
Thus, the values are:
- \( A = -6 \)
- \( B = -3 \)
- [tex]\( C = 2 \)[/tex]
