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put this solution on YOUR website! Find the function y = ax^2 + bx + c whose graph contains the points:
(1,2), (-2,-7), and (2,-3).
:
Write an equation for each one in the form ax^2 = bx + c = y, using the x,y given:
x=1; 1a + 1b + c = 2
x=-2: 4a - 2b + c =-7
x=2: 4a + 2b + c = -3
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Use elimination for find b
:
look at the 2nd and 3rd equations; subtracting eliminates a and c:
4a - 2b + c =-7
4a + 2b + c = -3
----------------------subtract
0a - 4b + 0c = -4
-4b = -4
b = -4/-4
b = + 1
:
Replace b with 1 in the 1st equation:
a + 1 + c = 2
a + c = 2 -1
a + c = 1
:
Do the same in the 2nd equation
4a - 2(1) + c = -7
4a - 2 + c = -7
4a + c = - 7 + 2
4a + c = -5
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Subtract (a + c = 1) from (4a + c = -5)
4a + c = -5
a + c = 1
--------------subtract
3a + 0c = -6
a = -6/3
a = -2
:
Find c using 1st equation substitute for a and b to find c:
-2 + 1 + c = 2
-1 + c = 2
c = 2 + 1
c = 3
:
a=-2; b= 1; c=3
Our quadratic is y = -2x^2 + x + 3
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Substitute and see if the 3 given coordinates are true of this equation
:
The graph should look like this
