Question 42982: 1. Determine the vertex of y=x^2-8x+22.
2. If P(4,-5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6).
3. An object is projected upward from the top of a tower. Its distance in feet above the ground after t seconds is given by s(t)=-16t^2+64t+80. How many seconds will it take to reach ground level?
4. Given f(x)=5x+7 and g(x) =x^2+7, find (g f)(x)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Determine the vertex of y=x^2-8x+22.
Put in vertex form by completing the square , as follows:
x^2-8x+16=y-6
(x+4)^2=y-6
Vertex = (h,k) = (-4,6)
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2. If P(4,-5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6).
Y get doubled and x moves 6 to the right so the point is (10,-10)
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3. An object is projected upward from the top of a tower. Its distance in feet above the ground after t seconds is given by s(t)=-16t^2+64t+80. How many seconds will it take to reach ground level?
Ground level means s=0.
0=-16(t^2-4t-5)
0=-16(t-5)(t+1)
t=5 sec. (time when object is on the ground)
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4. Given f(x)=5x+7 and g(x) =x^2+7, find (g f)(x)
g[f(x)]=g(5x+7)=(5x+7)^2+7=25x^2+70x+56
Cheers,
Stan H.
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