Question 1193889
Find the quadratic function that fits the data points (1,6) (-1,2) and (3,34).
Using the form ax^2 + bx + c = y, write an equation for each x,y point
1,6:  a + b + c = 6
-1,2: a - b + c = 2
3,34: 9a+3b + c = 34
:
add the 1st 2 equations
 a + b + c = 6
 a - b + c = 2
---------------
2a + 0 + 2c = 8
simplify, divide by 2
a + c = 4
:
multiply the 2nd equation by 3, add to the 3rd equation
3a - 3b + 3c = 6
9a + 3b +  c = 34
--------------------
12a + 0 + 4c = 40
simplify, divide by 2
6a + 2c = 20
:
Multiply (a+c=4) by 2, subtract from the above equation
6a + 2c = 20
2a + 2c = 8
--------------subtraction eliminates c, find a
4a + 0 = 12
a = 12/4
a = 3
:
a + c = 4
3 + c = 4
c = 1
and
a + b + c = 6
3 + b + 1 = 6
b = 6 - 4
b = 2
:
The equation: y = 3x^2 + 2x + 1