Question

What are the correct coordinates for the function g(x) =−3x^2−6x+x with the inputs of -4, -3, -2, and 0?
The coordinate (-4, Response area) , (-3, Response area), (-2, Response area), and (0,___)

Answer 1

To determine the coordinates for the function \( g(x) = -3x^2 - 6x + x \), we can first simplify the function:

\[
g(x) = -3x^2 - 6x + x = -3x^2 - 5x
\]

Next, we will evaluate \( g(x) \) at the specified inputs: -4, -3, -2, and 0.

1. **For \( x = -4 \)**:
\[
g(-4) = -3(-4)^2 - 5(-4)
= -3(16) + 20
= -48 + 20
= -28
\]
Coordinate: \((-4, -28)\)

2. **For \( x = -3 \)**:
\[
g(-3) = -3(-3)^2 - 5(-3)
= -3(9) + 15
= -27 + 15
= -12
\]
Coordinate: \((-3, -12)\)

3. **For \( x = -2 \)**:
\[
g(-2) = -3(-2)^2 - 5(-2)
= -3(4) + 10
= -12 + 10
= -2
\]
Coordinate: \((-2, -2)\)

4. **For \( x = 0 \)**:
\[
g(0) = -3(0)^2 - 5(0)
= 0
\]
Coordinate: \((0, 0)\)

Now we can write the coordinates for the function:

1. (-4, -28)
2. (-3, -12)
3. (-2, -2)
4. (0, 0)

So, the final answers can be summarized as:
- (-4, -28)
- (-3, -12)
- (-2, -2)
- (0, 0)