Question 1193889: Find the quadratic function that fits the data points (1,6) (-1,2) and (3,34).
Found 3 solutions by ankor@dixie-net.com, MathTherapy, Alan3354:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website! Find the quadratic function that fits the data points (1,6) (-1,2) and (3,34).
Equation of a PARABOLA: y = ax2 + bx + c
6 = a(1)2 + b(1) + c ----- Substituting (1, 6) for (x, y)
6 = a + b + c ---- eq (i)
y = ax2 + bx + c
2 = a(- 1)2 + b(- 1) + c ----- Substituting (- 1, 2) for (x, y)
2 = a - b + c ---- eq (ii)
y = ax2 + bx + c
34 = a(3)2 + b(3) + c ----- Substituting (3, 34) for (x, y)
34 = 9a + 3b + c ---- eq (iii)
6 = a + b + c ------ eq (i)
2 = a - b + c ------ eq (ii)
34 = 9a + 3b + c --- eq (iii)
4 = 2b ---- Subtracting eq (ii) from eq (i)
32 = 8a + 4b ----- Subtracting eq (ii) from eq (iii) ---- eq (iv)
32 = 8a + 4(2) --- Substituting 2 for b in eq (iv)
6 = 3 + 2 + c ---- Substituting 3 for a, and 2 for b in eq (i)
6 = 5 + c
1 = c
Equation of a PARABOLA: y = ax2 + bx + c
y = 3x2 + 2x + 1 ------- Substituting 3 for a, 2 for b, and 1 for c
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Find the quadratic function that fits the data points (1,6) (-1,2) and (3,34).
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I have an Excel sheet that does that.
Also circles.
You want a copy?
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