SOLUTION:

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Question 188748:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 2

c)

In order to graph y=x%5E2-6x-7, we need to plot a few points.


Let's find the y value when x=-1


y=x%5E2-6x-7 Start with the given equation.


y=%28-1%29%5E2-6%28-1%29-7 Plug in x=-1.


y=1-6%28-1%29-7 Square -1 to get 1.


y=1%2B6-7 Multiply -6 and -1 to get 6.


y=0 Combine like terms.


So when x=-1, y=0. So we have the point (-1,0).


----------------------------


Let's find the y value when x=0


y=x%5E2-6x-7 Start with the given equation.


y=%280%29%5E2-6%280%29-7 Plug in x=0.


y=0-6%280%29-7 Square 0 to get 0.


y=0%2B0-7 Multiply -6 and 0 to get 0.


y=-7 Combine like terms.


So when x=0, y=-7. So we have the point (0,-7).


----------------------------


Let's find the y value when x=1


y=x%5E2-6x-7 Start with the given equation.


y=%281%29%5E2-6%281%29-7 Plug in x=1.


y=1-6%281%29-7 Square 1 to get 1.


y=1-6-7 Multiply -6 and 1 to get -6.


y=-12 Combine like terms.


So when x=1, y=-12. So we have the point (1,-12).


----------------------------


Let's find the y value when x=2


y=x%5E2-6x-7 Start with the given equation.


y=%282%29%5E2-6%282%29-7 Plug in x=2.


y=4-6%282%29-7 Square 2 to get 4.


y=4-12-7 Multiply -6 and 2 to get -12.


y=-15 Combine like terms.


So when x=2, y=-15. So we have the point (2,-15).


----------------------------


Let's find the y value when x=3


y=x%5E2-6x-7 Start with the given equation.


y=%283%29%5E2-6%283%29-7 Plug in x=3.


y=9-6%283%29-7 Square 3 to get 9.


y=9-18-7 Multiply -6 and 3 to get -18.


y=-16 Combine like terms.


So when x=3, y=-16. So we have the point (3,-16).


----------------------------


Let's find the y value when x=4


y=x%5E2-6x-7 Start with the given equation.


y=%284%29%5E2-6%284%29-7 Plug in x=4.


y=16-6%284%29-7 Square 4 to get 16.


y=16-24-7 Multiply -6 and 4 to get -24.


y=-15 Combine like terms.


So when x=4, y=-15. So we have the point (4,-15).


----------------------------


Let's find the y value when x=5


y=x%5E2-6x-7 Start with the given equation.


y=%285%29%5E2-6%285%29-7 Plug in x=5.


y=25-6%285%29-7 Square 5 to get 25.


y=25-30-7 Multiply -6 and 5 to get -30.


y=-12 Combine like terms.


So when x=5, y=-12. So we have the point (5,-12).


----------------------------


Let's find the y value when x=6


y=x%5E2-6x-7 Start with the given equation.


y=%286%29%5E2-6%286%29-7 Plug in x=6.


y=36-6%286%29-7 Square 6 to get 36.


y=36-36-7 Multiply -6 and 6 to get -36.


y=-7 Combine like terms.


So when x=6, y=-7. So we have the point (6,-7).


----------------------------


Let's find the y value when x=7


y=x%5E2-6x-7 Start with the given equation.


y=%287%29%5E2-6%287%29-7 Plug in x=7.


y=49-6%287%29-7 Square 7 to get 49.


y=49-42-7 Multiply -6 and 7 to get -42.


y=0 Combine like terms.


So when x=7, y=0. So we have the point (7,0).


----------------------------


Now let's make a table of the values we just found.


Table of Values:





xy
-10


0-7


1-12


2-15


3-16


4-15


5-12


6-7


70

Now let's plot the points:




Now draw a curve through all of the points to graph y=x%5E2-6x-7:


Graph of y=x%5E2-6x-7


-------------------------------------------

# 2

d)

In order to graph y=x%5E2-4x-5, we need to plot a few points.


Let's find the y value when x=-2


y=x%5E2-4x-5 Start with the given equation.


y=%28-2%29%5E2-4%28-2%29-5 Plug in x=-2.


y=4-4%28-2%29-5 Square -2 to get 4.


y=4%2B8-5 Multiply -4 and -2 to get 8.


y=7 Combine like terms.


So when x=-2, y=7. So we have the point (-2,7).


----------------------------


Let's find the y value when x=-1


y=x%5E2-4x-5 Start with the given equation.


y=%28-1%29%5E2-4%28-1%29-5 Plug in x=-1.


y=1-4%28-1%29-5 Square -1 to get 1.


y=1%2B4-5 Multiply -4 and -1 to get 4.


y=0 Combine like terms.


So when x=-1, y=0. So we have the point (-1,0).


----------------------------


Let's find the y value when x=0


y=x%5E2-4x-5 Start with the given equation.


y=%280%29%5E2-4%280%29-5 Plug in x=0.


y=0-4%280%29-5 Square 0 to get 0.


y=0%2B0-5 Multiply -4 and 0 to get 0.


y=-5 Combine like terms.


So when x=0, y=-5. So we have the point (0,-5).


----------------------------


Let's find the y value when x=1


y=x%5E2-4x-5 Start with the given equation.


y=%281%29%5E2-4%281%29-5 Plug in x=1.


y=1-4%281%29-5 Square 1 to get 1.


y=1-4-5 Multiply -4 and 1 to get -4.


y=-8 Combine like terms.


So when x=1, y=-8. So we have the point (1,-8).


----------------------------


Let's find the y value when x=2


y=x%5E2-4x-5 Start with the given equation.


y=%282%29%5E2-4%282%29-5 Plug in x=2.


y=4-4%282%29-5 Square 2 to get 4.


y=4-8-5 Multiply -4 and 2 to get -8.


y=-9 Combine like terms.


So when x=2, y=-9. So we have the point (2,-9).


----------------------------


Let's find the y value when x=3


y=x%5E2-4x-5 Start with the given equation.


y=%283%29%5E2-4%283%29-5 Plug in x=3.


y=9-4%283%29-5 Square 3 to get 9.


y=9-12-5 Multiply -4 and 3 to get -12.


y=-8 Combine like terms.


So when x=3, y=-8. So we have the point (3,-8).


----------------------------


Let's find the y value when x=4


y=x%5E2-4x-5 Start with the given equation.


y=%284%29%5E2-4%284%29-5 Plug in x=4.


y=16-4%284%29-5 Square 4 to get 16.


y=16-16-5 Multiply -4 and 4 to get -16.


y=-5 Combine like terms.


So when x=4, y=-5. So we have the point (4,-5).


----------------------------


Let's find the y value when x=5


y=x%5E2-4x-5 Start with the given equation.


y=%285%29%5E2-4%285%29-5 Plug in x=5.


y=25-4%285%29-5 Square 5 to get 25.


y=25-20-5 Multiply -4 and 5 to get -20.


y=0 Combine like terms.


So when x=5, y=0. So we have the point (5,0).


----------------------------


Let's find the y value when x=6


y=x%5E2-4x-5 Start with the given equation.


y=%286%29%5E2-4%286%29-5 Plug in x=6.


y=36-4%286%29-5 Square 6 to get 36.


y=36-24-5 Multiply -4 and 6 to get -24.


y=7 Combine like terms.


So when x=6, y=7. So we have the point (6,7).


----------------------------


Now let's make a table of the values we just found.


Table of Values:





xy
-27


-10


0-5


1-8


2-9


3-8


4-5


50


67

Now let's plot the points:




Now draw a curve through all of the points to graph y=x%5E2-4x-5:


Graph of y=x%5E2-4x-5