SOLUTION: My teacher gave us this table. x 1 -2 0 -1 2 3 -4 4 -3 y ? 14 18 ? ? 9 ? ? ? I need to find the y-values with the questions mark and find a rule for this table.

Question 226922: My teacher gave us this table.
x 1 -2 0 -1 2 3 -4 4 -3
y ? 14 18 ? ? 9 ? ? ?
I need to find the y-values with the questions mark and find a rule for this table.
PLEASE HELP ME!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
x 1 -2 0 -1 2 3 -4 4 -3
y ? 14 18 ? ? 9 ? ? ?
:
Assuming this is a parabola, find the quadratic equation using the form: ax^2 = bx + c = y; this will be the rule.
we have x=0, y=18, (y intercept)so we know that c=18
:
Write to two equations using the given coordinates
x=-2,y=14
(-2^2)a - 2b + 18 = 14
4a - 2b + 18 = 14
4a - 2b = 14 - 18
4a - 2b = -4
and
x=3,y=9
3^2a + 3b + 18 = 9
9a + 3b = 9 - 18
9a + 3b = -9
:
Use elimination; multiply the 1st eq by 3, the 2nd equation by 2
12a - 6b = -12
18a + 6b = -18
-----------------addition eliminates b, find a
30a = -30
a = -1
;
Find b using 9a + 3b = -9
9(-1) +3b = -9
3b = -9 + 9
b = 0
:
This makes the equation; y = -x^2 + 18 , complete the table using this
:
x | y
------
1 |17
-2|14
0 |18
-1| 17
2 | 14
3 | 9
-4| 2
4 | 2
-3| 9
:
Will look like this

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