Answer:
The closest choice is ...
C) 27.48 and 5.20
Step-by-step explanation:
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}
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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.
