Consider g(x) = − (x + 6)2−2

Question

Part A: Identify the vertex

(1 point)
The vertex is the ordered pair:

Answer 1

The function given is \( g(x) = -(x + 6)^2 - 2 \).

This function is in the vertex form of a quadratic equation, which is \( g(x) = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.

From the given function:

• \( a = -1 \)
• \( h = -6 \) (since \( x + 6 \) can be rewritten as \( x - (-6) \))
• \( k = -2 \)

Thus, the vertex of the function \( g(x) \) is the ordered pair:

\[ \text{Vertex} = (-6, -2) \]

Answer 2

Part B. Complete the table(5 points)
its a box with 2 sides and 5 columns. the first column says X and below it has -10, -8, -6, -4, -2. And the other colum ur supposed to feel it it and it has g(x)

Answer 3

To complete the table, we need to evaluate \( g(x) = - (x + 6)^2 - 2 \) for each value of \( x \) provided. Let's calculate \( g(x) \) for each given \( x \):

1. For \( x = -10 \): \[ g(-10) = -((-10) + 6)^2 - 2 = -(-4)^2 - 2 = -16 - 2 = -18 \]

2. For \( x = -8 \): \[ g(-8) = -((-8) + 6)^2 - 2 = -(-2)^2 - 2 = -4 - 2 = -6 \]

3. For \( x = -6 \): \[ g(-6) = -((-6) + 6)^2 - 2 = -(0)^2 - 2 = 0 - 2 = -2 \]

4. For \( x = -4 \): \[ g(-4) = -((-4) + 6)^2 - 2 = -(2)^2 - 2 = -4 - 2 = -6 \]

5. For \( x = -2 \): \[ g(-2) = -((-2) + 6)^2 - 2 = -(4)^2 - 2 = -16 - 2 = -18 \]

Now, we can summarize the results in the table:

| \( x \) | \( g(x) \) | |:----------:|:----------:| | -10 | -18 | | -8 | -6 | | -6 | -2 | | -4 | -6 | | -2 | -18 |

Feel free to format it however you need!