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