Questions: Complete the table using the quadratic pattern given that (-2,1) is the vertex. Then, identify the x-intercepts of the quadratic function represented in the table. x -5 -4 -3 -2 ? ? ? y -8 -3 0 1 0 -3 -8 Complete the table. x -5 -4 -3 -2 y -8 -3 0 1 0 -3 -8

Solution Steps

To complete the table, we need to recognize the symmetry of the quadratic function around its vertex. Given that \((-2, 1)\) is the vertex, the values of \(y\) will mirror around \(x = -2\). We can use this symmetry to fill in the missing \(x\) values and corresponding \(y\) values.

1. Identify the vertex \((-2, 1)\) and note the symmetry of the quadratic function.
2. Use the given \(y\) values to determine the corresponding \(x\) values by reflecting them around the vertex.
3. Fill in the missing \(x\) values in the table.

The vertex of the quadratic function is given as \((-2, 1)\). This point indicates the maximum or minimum value of the function, which is \(y = 1\) when \(x = -2\).

Given the symmetry of the quadratic function around the vertex, we can find the missing \(x\) values and their corresponding \(y\) values. The \(x\) values are reflected around the vertex \(x = -2\):

• For \(x = -3\) (which is 1 unit left of the vertex), the corresponding \(y\) value is \(0\).
• For \(x = -1\) (which is 1 unit right of the vertex), the corresponding \(y\) value is also \(0\).
• For \(x = 0\) (which is 2 units right of the vertex), the corresponding \(y\) value is \(-3\).
• For \(x = 1\) (which is 3 units right of the vertex), the corresponding \(y\) value is \(-8\).

Thus, the completed table is:

\[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -5 & -4 & -3 & -2 & -1 & 0 & 1 \\ \hline y & -8 & -3 & 0 & 1 & 0 & -3 & -8 \\ \hline \end{array} \]

The \(x\)-intercepts occur where \(y = 0\). From the completed table, we see that:

• \(y = 0\) at \(x = -3\) and \(x = -1\).

Final Answer