Use the data set to create a quadratic function if it applies. use the model to predict the value of x when y = -4. (-3, 10), (0, 4), (3, -1), (6, -5), (9, -8) question 3 options: a) 29.32 and 3.97 b) 32.27 and 4.57 c) 27.48 and 5.20 d) no solution

The closest choice is ...

C)  27.48 and 5.20

Using the equation ...

  y = ax² + bx + c

You can substitute the first three points to get linear equations in a, b, and c.

  10 = a(-3)² +b(-3) +c = 9a -3b +c

  4 = a(0)² + b(0) +c = c

  -1 = a(3)² + b(3) +c = 9a +3b +c

The second equation tells us c=4. Subtracting the first equation from the last, we get ...

  (9a +3b +c) -(9a -3b +c) = (-1) -(10)

  6b = -11

  b = -11/6

Then we can find "a" from the first equation:

  10 = 9a -3(-11/6) +4

  1/2 = 9a . . . . subtract 19/2

  1/18 = a . . . . . divide by 9

The model is ...

  y = (1/18)x² -(11/6)x +4 . . . . . . . . [call this "model A"]

  y = (x² -33x +72)/18

Solving this for y = -4, we have ...

  -4 = (x² -33x +72)/18

  x² -33x +144 = 0 . . . . . . multiply by 18, add 72

  (x -16.5)² -128.25 = 0 . . . . put in vertex form

  x = 16.5 ±√128.25 ≈ {5.17525, 27.8248}

___

The closest values to these among the choices offered are those of choice C. It appears that the coefficients of model A were rounded to 3 decimal places (or so) before the predicted x-values were computed.

4 adults and 12 babies

step-by-step explanation:

4 x 7 = 28

12 x 15 = 180

180 + 28 =208

4 x 3 = 12

not enough information

step-by-step explanation:

we cannot know this, because the other students could have handed out 10 flyers, or they could have handed out 100. one way, the mean would go up, and another way, the mean would go down.