What are the correct coordinates for the function g(h)=−6h2−2h+h

Question

What are the correct coordinates for the function  g(h)=−6h2−2h+h
  with inputs of  −8
 ,  −6
 ,  −4
 ,  −2
 , and 0?(1 point)
Responses

(−376,−8)
, (−210,−6)
, (−92,−4)
, (−30,−2)
, (0,0)
      left parenthesis negative 376 comma negative 8 right parenthesis ,  left parenthesis negative 210 comma negative 6 right parenthesis ,  left parenthesis negative 92 comma negative 4 right parenthesis ,  left parenthesis negative 30 comma negative 2 right parenthesis ,  left parenthesis 0 comma 0 right parenthesis

(−8,−104)
, (−6,78)
, (−4,52)
, (−2,26)
, (0,0)
    left parenthesis negative 8 comma negative 104 right parenthesis ,  left parenthesis negative 6 comma 78 right parenthesis ,  left parenthesis negative 4 comma 52 right parenthesis ,  left parenthesis negative 2 comma 26 right parenthesis ,  left parenthesis 0 comma 0 right parenthesis

(−8,−376)
, (−6,−210)
, (−4,−92)
, (−2,−22)
, (0,0)
left parenthesis negative 8 comma negative 376 right parenthesis ,  left parenthesis negative 6 comma negative 210 right parenthesis ,  left parenthesis negative 4 comma negative 92 right parenthesis ,  left parenthesis negative 2 comma negative 22 right parenthesis ,  left parenthesis 0 comma 0 right parenthesis

(−8,−360)
, (−6,−198)
, (−4,−84)
, (−2,−6)
, (0,0)

GPT-4o mini · Answer

To find the coordinates for the function $g (h) = - 6 h^{2} - 2 h + h$ with the given inputs of $- 8, - 6, - 4, - 2,$ and $0$ , we will first simplify the function:

$g (h) = - 6 h^{2} - 2 h + h = - 6 h^{2} - h$

Now, we will calculate $g (h)$ for each input:

Input: $h = - 8$ $g (- 8) = - 6 (- 8)^{2} - (- 8) = - 6 \cdot 64 + 8 = - 384 + 8 = - 376$ Coordinate: $(- 376, - 8)$
Input: $h = - 6$ $g (- 6) = - 6 (- 6)^{2} - (- 6) = - 6 \cdot 36 + 6 = - 216 + 6 = - 210$ Coordinate: $(- 210, - 6)$
Input: $h = - 4$ $g (- 4) = - 6 (- 4)^{2} - (- 4) = - 6 \cdot 16 + 4 = - 96 + 4 = - 92$ Coordinate: $(- 92, - 4)$
Input: $h = - 2$ $g (- 2) = - 6 (- 2)^{2} - (- 2) = - 6 \cdot 4 + 2 = - 24 + 2 = - 22$ Coordinate: $(- 22, - 2)$
Input: $h = 0$ $g (0) = - 6 (0)^{2} - (0) = 0$ Coordinate: $(0, 0)$

Thus, the resulting coordinates are:

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

From the options given, the closest match is:

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

So, the correct selection is: (−8, −376), (−6, −210), (−4, −92), (−2, −22), (0, 0).