Question 705760: Someone PLEASE help me!I'm am all sorts of confused on these. Can anyone help me out and show me how do get to these?
1. Given the following quadratic equation, find
a. the vertex
b. the axis of symmetry
c. the intercepts
d. the domain
e. the range
f. the interval where the function is increasing, and
g. the interval where the function is decreasing
h. Graph the function.
y=-x^2+2x+8
2. Given the following rational function, find
a. the horizontal asymptote(s),
b. the vertical asymptote(s), if any, and
c. the oblique asymptote(s), if any.
f(x)=6/(x-5)
Found 3 solutions by stanbon, lynnlo, solver91311:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Given the following quadratic equation
y = -x^2+2x+8
-----
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
----------------------------
a. the vertex::(1,9)
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b. the axis of symmetry:: x = 1
------------------------
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
----------------------
y-int:
Let x = 0, then y = 8
===========================
d. the domain:: All Real Numbers
----------------------------
e. the range:: y <= 9
-------------------------------
f. the interval where the function is increasing:: x < 1
-------------------------------
g. the interval where the function is decreasing:: x > 1
-------------------------------
h. Graph the function.
y=-x^2+2x+8
---------------------------------------
2. Given the following rational function
f(x)=6/(x-5)
a. the horizontal asymptote(s):: y = 0/1 = 0
---------------------------------------
b. the vertical asymptote(s):: x = 5
---------------------------------------
c. the oblique asymptote(s):: none
=================
Cheers,
Stan H.
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Answer by lynnlo(4176) (Show Source):
You can put this solution on YOUR website! PART 1
(1)(1,9)
(2)X=1
(3)X IS (-2,0)(4,0)
Y IS (0,8)
(4) ALL REAL NUMBERS
(5) Y<9--MAKE SURE YOU PUT A LINE UNDER THE<
(6)INCREASING(X<1)
(7)DECREASING(X>1)
PART 2
F(X)=6/(X-5)
(1)Y=0
(2)X=5
(3)NONE
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Given the quadratic function 
First, determine the  -coordinate of the vertex.
Then determine the  -coordinate of the vertex.
\ =\ a(x_v)^2\ +\ b(x_v)\ +\ c)
Then determine the -coordinate of the -intercept which is equal to:
\ =\ a(0)^2\ +\ b(0)\ +\ c\ =\ c)
Then set the function equal to zero and solve the resulting quadratic equation:
Then determine whether the graph opens upwards or downwards. If the lead coefficient, that is  is positive, the graph opens upward, otherwise it opens downward.
With the above information you can answer all of the questions:
1. Vertex: )
2. Axis of symmetry: 
3. Intercepts: ) , ) , and )
4. Domain: The domain of all polynomial functions is the set of real numbers.
5. Range: If the graph opens upward, then the range is  . If the graph opens downward, then the range is 
6. Increasing interval: if graph opens upward, the increasing interval is from  to  . If the graph opens downward, the increasing interval is from  to .
7. Decreasing interval: reverse the answers to 6. above.
8. Plot the vertex, the y-intercept, and the two x-intercepts. Use symmetry to plot ) . Draw a smooth curve through the 5 plotted points.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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