Question 705760
1. Given the following quadratic equation
y = -x^2+2x+8
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y = -(x^2-2x+?) + 8 + ?
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y = -(x^2-2x+1) + 8 + 1
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y = -(x-1)^2 + 9
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a. the vertex::(1,9)
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b. the axis of symmetry:: x = 1
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c. the intercepts
x-int: 
Solve -x^2+2x+8 = 0
x = [-2 +- sqrt(2^2-4*-1*8)]/(-2)
x = [-2 +- sqrt(4+32)]/(-2)
x = [-2 +- 6]/(-2)
x = 4 or x = -2
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y-int:
Let x = 0, then y = 8
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d. the domain:: All Real Numbers
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e. the range:: y <= 9
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f. the interval where the function is increasing:: x < 1
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g. the interval where the function is decreasing:: x > 1
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h. Graph the function. 
y=-x^2+2x+8
{{{graph(400,400,-10,10,-10,15,-x^2+2x+8)}}}
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2.  Given the following rational function
f(x)=6/(x-5)
 
a. the horizontal asymptote(s):: y = 0/1 = 0
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b. the vertical asymptote(s):: x = 5
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c. the oblique asymptote(s):: none
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Cheers,
Stan H.
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