Question

To find the coordinates for the function \( g(h) = -6h^2 - 2h + h \), I need to plug in some values for \( h \) and calculate the results. Let's do that for \( h = -8, -6, -4, -2, \) and \( 0 \).

1. **For \( h = -8 \)**:
\[
g(-8) = -6(-8)^2 - 2(-8) + (-8)
\]
First, calculate \((-8)^2\):
\[
g(-8) = -6(64) + 16 - 8
\]
Now, multiply:
\[
g(-8) = -384 + 16 - 8
\]
Then, add them up:
\[
g(-8) = -384 + 8 = -376
\]
So, the coordinate is **(-8, -376)**.

2. **For \( h = -6 \)**:
\[
g(-6) = -6(-6)^2 - 2(-6) + (-6)
\]
Calculate \((-6)^2\):
\[
g(-6) = -6(36) + 12 - 6
\]
Now, multiply:
\[
g(-6) = -216 + 12 - 6
\]
Add them:
\[
g(-6) = -216 + 6 = -210
\]
So, the coordinate is **(-6, -210)**.

3. **For \( h = -4 \)**:
\[
g(-4) = -6(-4)^2 - 2(-4) + (-4)
\]
Calculate \((-4)^2\):
\[
g(-4) = -6(16) + 8 - 4
\]
Now, multiply:
\[
g(-4) = -96 + 8 - 4
\]
Add them:
\[
g(-4) = -96 + 4 = -92
\]
So, the coordinate is **(-4, -92)**.

4. **For \( h = -2 \)**:
\[
g(-2) = -6(-2)^2 - 2(-2) + (-2)
\]
Calculate \((-2)^2\):
\[
g(-2) = -6(4) + 4 - 2
\]
Now, multiply:
\[
g(-2) = -24 + 4 - 2
\]
Add them:
\[
g(-2) = -24 + 2 = -22
\]
So, the coordinate is **(-2, -22)**.

5. **For \( h = 0 \)**:
\[
g(0) = -6(0)^2 - 2(0) + 0
\]
Since everything is multiplied by 0:
\[
g(0) = 0
\]
So, the coordinate is **(0, 0)**.

---

Therefore, the coordinates for the function \( g(h) \) with the inputs \( -8, -6, -4, -2, \) and \( 0 \) are:

- (-8, -376)
- (-6, -210)
- (-4, -92)
- (-2, -22)
- (0, 0)
\
compact this

Answer 1

Here are the coordinates for the function \( g(h) = -6h^2 - 2h + h \) with the specified inputs:

- For \( h = -8 \): **(-8, -376)**
- For \( h = -6 \): **(-6, -210)**
- For \( h = -4 \): **(-4, -92)**
- For \( h = -2 \): **(-2, -22)**
- For \( h = 0 \): **(0, 0)**

In summary, the coordinates are:

- (-8, -376)
- (-6, -210)
- (-4, -92)
- (-2, -22)
- (0, 0)