SOLUTION: find the quadratic function y = ax ^ 2 + bx + c whose graph passes through the given points. (1,-1)(-1,-9)(-2,-10) thanks in advance for the help!

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Question 929710: find the quadratic function y = ax ^ 2 + bx + c whose graph passes through the given points.
(1,-1)(-1,-9)(-2,-10)


thanks in advance for the help!

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
to find the quadratic function y+=+ax+%5E+2+%2B+bx+%2B+c whose graph passes through the given points (1,-1)(-1,-9)(-2,-10), we need to find a,b,and a and we can do it using given points
y+=+ax+%5E+2+%2B+bx+%2B+c ...plug in x=1 and y=-1 from (1,-1)
-1+=+a%2A1+%5E+2+%2B+b%2A1+%2B+c
-1+=+a+%2B+b+%2B+c.........eq.1

y+=+ax+%5E+2+%2B+bx+%2B+c ...plug in x=-1 and y=-9 from (-1,-9)
-9=+a%28-1%29%5E2+%2Bb%28-1%29+%2B+c
-9=+a+-b+%2B+c.........eq.2

y+=+ax+%5E+2+%2B+bx+%2B+c ...plug in x=-2 and y=-10 from (-2,-10)
-10=+a%28-2%29+%5E+2+%2B+b%28-2%29+%2B+c
-10=+4a+-2b+%2B+c..........eq.3

you have a system:
-1+=+a+%2B+b+%2B+c.........eq.1
-9=+a+-b+%2B+c.........eq.2
-10=+4a+-2b+%2B+c..........eq.3
_______________________________
start with
-1+=+a+%2B+b+%2B+c.........eq.1
-9=+a+-b+%2B+c.........eq.2
___________________________subtract 2 from 1
-1-%28-9%29+=+a-a+%2B+b-%28-b%29+%2B+c-c
-1%2B9+=+cross%28a%29-cross%28a%29+%2B+b%2Bb+%2B+cross%28c%29-cross%28c%29
8+=+2b
8%2F2+=+b
highlight%28b=4%29
go to -10=+4a+-2b+%2B+c..........eq.3, plug in b
-10=+4a+-2%2A4+%2B+c
-10=+4a+-8+%2B+c
-10%2B8=+4a%2B+c
-2=+4a%2B+c
-2-4a=c
c=-2-4a
go to -1+=+a+%2B+b+%2B+c.........eq.1 substitute b and c
-1+=+a+%2B+4+-2-4a
-1+=+2+-3a
3a+=2%2B1
3a+=+3
highlight%28a+=1%29
go to c=-2-4a plug in a and find c
c=-2-4%281%29
c=-2-4
highlight%28c=-6%29
so, your equation is: y+=+x+%5E+2+%2B+4x+-6


(1,-1)(-1,-9)(-2,-10)