Question 200881: Find a quadratic funtion in the form y=ax^2+bx+c That passes through the points (-3,-13),(-1,-1),(2,32)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Find a quadratic funtion in the form y=ax^2+bx+c
That passes through the points (-3,-13),(-1,-1),(2,32)
:
Write an equation for each set of coordinates:
:
x = -3; y = -13
9a - 3b + c = -13
:
x = -1; y = -1
a - b + c = -1
:
x = 2; y = 32
4a + 2b + c = 32
:
Subtract the 2nd equation from the 1st equation
9a - 3b + c = -13
a - b + c = -1
----------------eliminates c
8a - 2b = -12
:
Subtract the 2nd equation from the 3rd equation
4a + 2b + c = 32
a - b + c = -1
-----------------eliminates c
3a + 3b = 33
Simplify,divide by 3
a + b = 11
:
multiply above equation by 2, add to
8a - 2b = -12
2a + 2b = 22
-------------eliminates b
10a = 10
a = 1
:
Find b using a + b = 11
1 + b = 11
b = 11 - 1
b = 10
;
find c using a - b + c = -1
1 - 10 + c = -1
-9 + c = -1
c = -1 + 9
c = 8
:
The equation: y = x^2 + 10x + 8
:
Prove this to yourself by substituting the given values for x and finding y
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