Question

Create a graph, then answer the following question. What are the key points on the graph of y = x ^ 2 - 8 ? Name the vertex, x-intercept(s), and y-intercept. (1 point) x-intercepts: (0, 0)(8, 0) Oy-intercept: (0,0) vertex (4, - 16) x-intercept: (4, - 16) Oy-intercept: (0,0) vertex (8, 0) x-intercept: (0,8) Oy-intercept: (0,0) vertex: (4, - 16) x-intercepts: (0,0) (0,8) Overtex (4 ,-16) There is no y-intercept

Answer 1

To analyze the graph of the quadratic equation \( y = x^2 - 8 \), let's determine the key points: the vertex, x-intercepts, and y-intercept.

1. **Vertex**:
The vertex of a quadratic function in the form \( y = ax^2 + bx + c \) can be found using the formula \( x = -\frac{b}{2a} \). In this case, \( a = 1 \), \( b = 0 \), and \( c = -8 \).

\[
x = -\frac{0}{2 \cdot 1} = 0
\]

Now, substituting \( x = 0 \) back into the equation to find \( y \):

\[
y = (0)^2 - 8 = -8
\]

Thus, the vertex is at \( (0, -8) \).

2. **Y-intercept**:
To find the y-intercept, set \( x = 0 \):

\[
y = 0^2 - 8 = -8
\]

Therefore, the y-intercept is at \( (0, -8) \).

3. **X-intercepts**:
To find the x-intercepts, set \( y = 0 \):

\[
0 = x^2 - 8
\]

\[
x^2 = 8
\]

\[
x = \pm\sqrt{8} = \pm 2\sqrt{2}
\]

Thus, the x-intercepts are at \( (2\sqrt{2}, 0) \) and \( (-2\sqrt{2}, 0) \).

### Summary of Key Points:
- **Vertex**: \( (0, -8) \)
- **X-intercepts**: \( (2\sqrt{2}, 0) \) and \( (-2\sqrt{2}, 0) \)
- **Y-intercept**: \( (0, -8) \)

The provided answers in your question seem to be incorrect, especially regarding the vertex and intercepts. Here’s the correct summary once more:

1. **Vertex**: \( (0, -8) \)
2. **X-intercepts**: \( (2\sqrt{2}, 0) \) and \( (-2\sqrt{2}, 0) \)
3. **Y-intercept**: \( (0, -8) \)