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Question 531388: I need to graph: g(x)=-1/2f(x+1)-3 and show 3 ordered pairs.
Thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I need to graph: g(x)=-1/2f(x+1)-3 and show 3 ordered pairs.
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Define f(x) = ? ; the three coordinates of f(x) are (-5,4), (4,1) and (1,-2)
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ax^2 + bx + c = y
25a -5b+c = 4
16a +4b+c = 1
a + b + c = -2
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Use any method to find a,b,c
a =1/3
b =1/3
c =-8/3
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f(x) = (1/3)(x^2 + x - 8)
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So, f(x+1) = (1/3)(x^2+2x+1+x+1-8) = (1/3)(x^2+3x-7)
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Then g(x)= -1/2f(x+1)-3
g(x) = (-1/6)(x^2+3x-7)-3
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g(x) = (-1/6)x^2-(1/2)x -11/6
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Points:
g(0) = -11**6
g(1) = -1/6 - 1/2 - 11/6 = -15/6 = -5/2
g(-1) = (-1/6) + 1/2 - 11/6 = -3/2
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Cheers,
Stan H.
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