Question 643393: hi! please help me solve this one...
In the xy-plane, the graph of y=x^2+bx+c is symmetric about the line x=3 (what is symmetric?) and passes through the point (5,2) . What is the Value of c ?
Thank you in advance :)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Symmetric means that one half of the graph reflects across this line to create the other half.
Notice how x = 3 is 2 units away from x = 5 (since 5-3 = 2). So if we have one point (5,2), then (1,2) is also on the parabola since this point has an x coordinate that is also 2 units away from x = 3 (and has the same y coordinate)
So again, we have 2 points (5,2) and (1,2) that lie on the parabola. We will use this information to find the values of b and c
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y=x^2+bx+c
2=(5)^2+b(5)+c ... Plug in (5,2), ie plug in x = 5 and y = 2
2=25+5b+c
Now solve for c
2=25+5b+c
2-25=5b+c
-23=5b+c
-23-5b=c
c = -23-5b
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Reset and plug in (1,2)
y=x^2+bx+c
2=(1)^2+b(1)+c ... Plug in (1,2), ie plug in x = 1 and y = 2
2=1+b+c
Now plug in c = -23-5b to get
2=1+b+(-23-5b)
2=1+b-23-5b
2=-22-4b
2+22 = -4b
24 = -4b
24/(-4) = b
-6 = b
b = -6
Finally, use this to find c
c = -23-5b
c = -23-5(-6)
c = -23+30
c = 7
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Answer:
So the values of b and c are: b = -6 and c = 7
which means that  becomes 
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