SOLUTION: The function f(x)=-4(x+2)^2+5 is transformed into the function g(x) by the rule g(x)=f(x-5)+7. What are the coordinates of the turning point of g(x)?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The function f(x)=-4(x+2)^2+5 is transformed into the function g(x) by the rule g(x)=f(x-5)+7. What are the coordinates of the turning point of g(x)?      Log On


   

Question 1064247: The function f(x)=-4(x+2)^2+5 is transformed into the function g(x) by the rule g(x)=f(x-5)+7. What are the coordinates of the turning point of g(x)?
Answer by stanbon(75887) About Me  (Show Source):
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The function f(x)=-4(x+2)^2+5 is transformed into the function g(x) by the rule g(x)=f(x-5)+7. What are the coordinates of the turning point of g(x)?
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f(x-5) = 4(x-3)^2+5
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So, g(x) = 4(x-3)^2+12 = 4(x^2-6x+9)+12 = 4x^2 - 24x + 48
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Ans: Turning point = (-b/(2a),g(-b/2a))
-b/(2a) = 24/8 = 3
g(3) = 4*9-24*3+48 = 36-72+48 = -36+48 = 12
Ans:: (3,12)
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Cheers,
Stan H.
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