Question

To find the coordinates for the function ( g(h) = -6h^2 - 2h + h ) with the given inputs, we need to evaluate the function at each input value. Let’s calculate:


For ( h = -8 ):
g(−8)=−6(−8)2−2(−8)+(−8)
g(−8)=−6(64)+16−8
g(−8)=−384+16−8
g(−8)=−376
So, the coordinate is ((-8, -376)).


For ( h = -6 ):
g(−6)=−6(−6)2−2(−6)+(−6)
g(−6)=−6(36)+12−6
g(−6)=−216+12−6
g(−6)=−210
So, the coordinate is ((-6, -210)).


For ( h = -4 ):
g(−4)=−6(−4)2−2(−4)+(−4)
g(−4)=−6(16)+8−4
g(−4)=−96+8−4
g(−4)=−92
So, the coordinate is ((-4, -92)).


For ( h = -2 ):
g(−2)=−6(−2)2−2(−2)+(−2)
g(−2)=−6(4)+4−2
g(−2)=−24+4−2
g(−2)=−22
So, the coordinate is ((-2, -22)).


For ( h = 0 ):
g(0)=−6(0)2−2(0)+0
g(0)=0
So, the coordinate is ((0, 0)).


Therefore, the coordinates for the function ( g(h) = -6h^2 - 2h + h ) with the inputs (-8, -6, -4, -2, \text{and } 0) are:

((-8, -376))
((-6, -210))
((-4, -92))
((-2, -22))
((0, 0))
make this like a 9th grader wrote it

Answer 1

Sure! Here’s a simpler version of your calculations that sounds like a 9th grader wrote it:

---

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)

That's it!