SOLUTION: Graph the equations. (1) y = x squared - 4x (2) y = -x + 1

Algebra ->  Graphs -> SOLUTION: Graph the equations. (1) y = x squared - 4x (2) y = -x + 1      Log On


   

Question 122812: Graph the equations.
(1) y = x squared - 4x
(2) y = -x + 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

In order to graph f%28x%29=1x%5E2-4x, we need to plot some points. To do that, we need to plug in some x values to get some y values


So let's find the first point:



f%28x%29=1x%5E2-4x Start with the given function


f%28-2%29=1%28-2%29%5E2-4%28-2%29 Plug in x=-2


f%28-2%29=1%2A4-4%2A-2 Raise -2 to the 2nd power to get 4


f%28-2%29=4-4%2A-2 Multiply 1 and 4 to get 4


f%28-2%29=4--8 Multiply 4 and -2 to get -8


f%28-2%29=12 Subtract -8 from 4 to get 12


So when x=-2, we have y=12


So our 1st point is (-2,12)


-------------- Let's find another point --------------


f%28x%29=1x%5E2-4x Start with the given function


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


f%28-1%29=1%2A1-4%2A-1 Raise -1 to the 2nd power to get 1


f%28-1%29=1-4%2A-1 Multiply 1 and 1 to get 1


f%28-1%29=1--4 Multiply 4 and -1 to get -4


f%28-1%29=5 Subtract -4 from 1 to get 5


So when x=-1, we have y=5


So our 2nd point is (-1,5)


-------------- Let's find another point --------------


f%28x%29=1x%5E2-4x Start with the given function


f%280%29=1%280%29%5E2-4%280%29 Plug in x=0


f%280%29=1%2A0-4%2A0 Raise 0 to the 2nd power to get 0


f%280%29=0-4%2A0 Multiply 1 and 0 to get 0


f%280%29=0-0 Multiply 4 and 0 to get 0


f%280%29=0 Subtract 0 from 0 to get 0


So when x=0, we have y=0


So our 3rd point is (0,0)


-------------- Let's find another point --------------


f%28x%29=1x%5E2-4x Start with the given function


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


f%281%29=1%2A1-4%2A1 Raise 1 to the 2nd power to get 1


f%281%29=1-4%2A1 Multiply 1 and 1 to get 1


f%281%29=1-4 Multiply 4 and 1 to get 4


f%281%29=-3 Subtract 4 from 1 to get -3


So when x=1, we have y=-3


So our 4th point is (1,-3)


-------------- Let's find another point --------------


f%28x%29=1x%5E2-4x Start with the given function


f%282%29=1%282%29%5E2-4%282%29 Plug in x=2


f%282%29=1%2A4-4%2A2 Raise 2 to the 2nd power to get 4


f%282%29=4-4%2A2 Multiply 1 and 4 to get 4


f%282%29=4-8 Multiply 4 and 2 to get 8


f%282%29=-4 Subtract 8 from 4 to get -4


So when x=2, we have y=-4


So our 5th point is (2,-4)


-------------- Let's find another point --------------


f%28x%29=1x%5E2-4x Start with the given function


f%283%29=1%283%29%5E2-4%283%29 Plug in x=3


f%283%29=1%2A9-4%2A3 Raise 3 to the 2nd power to get 9


f%283%29=9-4%2A3 Multiply 1 and 9 to get 9


f%283%29=9-12 Multiply 4 and 3 to get 12


f%283%29=-3 Subtract 12 from 9 to get -3


So when x=3, we have y=-3


So our 6th point is (3,-3)


-------------- Let's find another point --------------


f%28x%29=1x%5E2-4x Start with the given function


f%284%29=1%284%29%5E2-4%284%29 Plug in x=4


f%284%29=1%2A16-4%2A4 Raise 4 to the 2nd power to get 16


f%284%29=16-4%2A4 Multiply 1 and 16 to get 16


f%284%29=16-16 Multiply 4 and 4 to get 16


f%284%29=0 Subtract 16 from 16 to get 0


So when x=4, we have y=0


So our 7th point is (4,0)


-------------- Let's find another point --------------


f%28x%29=1x%5E2-4x Start with the given function


f%285%29=1%285%29%5E2-4%285%29 Plug in x=5


f%285%29=1%2A25-4%2A5 Raise 5 to the 2nd power to get 25


f%285%29=25-4%2A5 Multiply 1 and 25 to get 25


f%285%29=25-20 Multiply 4 and 5 to get 20


f%285%29=5 Subtract 20 from 25 to get 5


So when x=5, we have y=5


So our 8th point is (5,5)


-------------- Let's find another point --------------


f%28x%29=1x%5E2-4x Start with the given function


f%286%29=1%286%29%5E2-4%286%29 Plug in x=6


f%286%29=1%2A36-4%2A6 Raise 6 to the 2nd power to get 36


f%286%29=36-4%2A6 Multiply 1 and 36 to get 36


f%286%29=36-24 Multiply 4 and 6 to get 24


f%286%29=12 Subtract 24 from 36 to get 12


So when x=6, we have y=12


So our 9th point is (6,12)


Now lets make a table of the values we have calculated 



 xy



 -212
 

 -15
 

 00
 

 1-3
 

 2-4
 

 3-3
 

 40
 

 55
 

 612
Now plot the points



Now connect the points to graph y=1x%5E2-4x (note: the more points you plot, the easier it is to draw the graph)









# 2





Looking at y=-x%2B1 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-1 and the y-intercept is b=1


Since b=1 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -1, this means:

rise%2Frun=-1%2F1


which shows us that the rise is -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1



So starting at , go down 1 unit


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=-x%2B1

So this is the graph of y=-x%2B1 through the points and