Question

What are the correct coordinates for the function g of h equals negative 6h squared - 2H + h with inputs of negative 8, -6 -4 -2 and 0

Answer 1

To find the coordinates for the function \( g(h) = -6h^2 - 2h + h \) at the given inputs \( h = -8, -6, -4, -2, 0 \), we first simplify the function:

\[
g(h) = -6h^2 - 2h + h = -6h^2 - h
\]

Now, let's calculate \( g(h) \) for each value of \( h \):

1. **For** \( h = -8 \):

\[
g(-8) = -6(-8)^2 - (-8) = -6(64) + 8 = -384 + 8 = -376
\]

2. **For** \( h = -6 \):

\[
g(-6) = -6(-6)^2 - (-6) = -6(36) + 6 = -216 + 6 = -210
\]

3. **For** \( h = -4 \):

\[
g(-4) = -6(-4)^2 - (-4) = -6(16) + 4 = -96 + 4 = -92
\]

4. **For** \( h = -2 \):

\[
g(-2) = -6(-2)^2 - (-2) = -6(4) + 2 = -24 + 2 = -22
\]

5. **For** \( h = 0 \):

\[
g(0) = -6(0)^2 - (0) = 0
\]

Now, we can compile the coordinates for each value of \( h \):

- For \( h = -8 \), the coordinates are \( (-8, -376) \).
- For \( h = -6 \), the coordinates are \( (-6, -210) \).
- For \( h = -4 \), the coordinates are \( (-4, -92) \).
- For \( h = -2 \), the coordinates are \( (-2, -22) \).
- For \( h = 0 \), the coordinates are \( (0, 0) \).

So the final coordinates are:

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