SOLUTION: Help please, Find the equation of the quadratic function {{{y=ax^2+bx+c}}} whose graph runs through points (3,2),(4,3),(5,2)

Question 674561: Help please,
Find the equation of the quadratic function whose graph runs through points (3,2),(4,3),(5,2)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find the equation of the quadratic function y = ax^2 + bx+ c, whose graph runs through points (3,2),(4,3),(5,2)
:
Write a equation for each x,y pair, replacing x and y
3,2: 9a + 3b + c = 2
4,3: 16a + 4b + c = 3
5,2: 25a + 5b + c = 2
:
Use elimination and substitution
:
Subtract the 1st equation from the 2nd
16a + 4b + c = 3
9a + 3b + c = 2
-----------------Subtraction eliminates c
7a + b = 1
b = (1-7a), for substitution
:
Subtract the 1st equation from the 3rd
25a + 5b + c = 2
9a + 3b + c = 2
-----------------Subtraction eliminates c
16a + 2b = 0
Replace b with (1-7a)
16a + 2(1-7a) = 0
16a + 2 - 14a = 0
2a = -2
a = -1
:
Find b
b = 1 - 7(-1)
b = 1 + 7
b = 8
:
Find c using the 1st original equation
9(-1) + 3(8) + c = 2
-9 + 24 + c = 2
15 + c = 2
c = 2 - 15
c = -13
:
The equation, y = -x^2 + 8x - 13
:
:
YOu can confirm this, substitute for x and find y, for each given pair
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