SOLUTION: Graph the equation (1) y = -x squared +1 (2) y = 2x

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Question 122811: Graph the equation
(1) y = -x squared +1
(2) y = 2x
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%2B1, 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%2B1 Start with the given function


f%28-3%29=-1%28-3%29%5E2%2B1 Plug in x=-3


f%28-3%29=-1%2A9%2B1 Raise -3 to the 2nd power to get 9


f%28-3%29=-9%2B1 Multiply -1 and 9 to get -9


f%28-3%29=-8 Add -9 and 1 to get -8


So when x=-3, we have y=-8


So our 1st point is (-3,-8)


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


f%28x%29=-1x%5E2%2B1 Start with the given function


f%28-2%29=-1%28-2%29%5E2%2B1 Plug in x=-2


f%28-2%29=-1%2A4%2B1 Raise -2 to the 2nd power to get 4


f%28-2%29=-4%2B1 Multiply -1 and 4 to get -4


f%28-2%29=-3 Add -4 and 1 to get -3


So when x=-2, we have y=-3


So our 2nd point is (-2,-3)


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


f%28x%29=-1x%5E2%2B1 Start with the given function


f%28-1%29=-1%28-1%29%5E2%2B1 Plug in x=-1


f%28-1%29=-1%2A1%2B1 Raise -1 to the 2nd power to get 1


f%28-1%29=-1%2B1 Multiply -1 and 1 to get -1


f%28-1%29=0 Add -1 and 1 to get 0


So when x=-1, we have y=0


So our 3rd point is (-1,0)


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


f%28x%29=-1x%5E2%2B1 Start with the given function


f%280%29=-1%280%29%5E2%2B1 Plug in x=0


f%280%29=-1%2A0%2B1 Raise 0 to the 2nd power to get 0


f%280%29=0%2B1 Multiply -1 and 0 to get 0


f%280%29=1 Add 0 and 1 to get 1


So when x=0, we have y=1


So our 4th point is (0,1)


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


f%28x%29=-1x%5E2%2B1 Start with the given function


f%281%29=-1%281%29%5E2%2B1 Plug in x=1


f%281%29=-1%2A1%2B1 Raise 1 to the 2nd power to get 1


f%281%29=-1%2B1 Multiply -1 and 1 to get -1


f%281%29=0 Add -1 and 1 to get 0


So when x=1, we have y=0


So our 5th point is (1,0)


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


f%28x%29=-1x%5E2%2B1 Start with the given function


f%282%29=-1%282%29%5E2%2B1 Plug in x=2


f%282%29=-1%2A4%2B1 Raise 2 to the 2nd power to get 4


f%282%29=-4%2B1 Multiply -1 and 4 to get -4


f%282%29=-3 Add -4 and 1 to get -3


So when x=2, we have y=-3


So our 6th point is (2,-3)


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


f%28x%29=-1x%5E2%2B1 Start with the given function


f%283%29=-1%283%29%5E2%2B1 Plug in x=3


f%283%29=-1%2A9%2B1 Raise 3 to the 2nd power to get 9


f%283%29=-9%2B1 Multiply -1 and 9 to get -9


f%283%29=-8 Add -9 and 1 to get -8


So when x=3, we have y=-8


So our 7th point is (3,-8)


Now lets make a table of the values we have calculated 



 xy



 -3-8
 

 -2-3
 

 -10
 

 01
 

 10
 

 2-3
 

 3-8
Now plot the points



Now connect the points to graph y=-1x%5E2%2B1 (note: the more points you plot, the easier it is to draw the graph)








# 2


Looking at y=2x we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=2 and the y-intercept is b=0 note: y=2x really looks like y=2x%2B0


Since b=0 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 2, this means:

rise%2Frun=2%2F1


which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1



So starting at , go up 2 units


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



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

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