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)   (Show Source): You can put this solution on YOUR website!
# 1

In order to graph , 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:



Start with the given function


Plug in


Raise -3 to the 2nd power to get 9


Multiply -1 and 9 to get -9


Add -9 and 1 to get -8


So when , we have


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


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


Start with the given function


Plug in


Raise -2 to the 2nd power to get 4


Multiply -1 and 4 to get -4


Add -4 and 1 to get -3


So when , we have


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


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


Start with the given function


Plug in


Raise -1 to the 2nd power to get 1


Multiply -1 and 1 to get -1


Add -1 and 1 to get 0


So when , we have


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


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


Start with the given function


Plug in


Raise 0 to the 2nd power to get 0


Multiply -1 and 0 to get 0


Add 0 and 1 to get 1


So when , we have


So our 4th point is (0,1)


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


Start with the given function


Plug in


Raise 1 to the 2nd power to get 1


Multiply -1 and 1 to get -1


Add -1 and 1 to get 0


So when , we have


So our 5th point is (1,0)


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


Start with the given function


Plug in


Raise 2 to the 2nd power to get 4


Multiply -1 and 4 to get -4


Add -4 and 1 to get -3


So when , we have


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


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


Start with the given function


Plug in


Raise 3 to the 2nd power to get 9


Multiply -1 and 9 to get -9


Add -9 and 1 to get -8


So when , we have


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 (note: the more points you plot, the easier it is to draw the graph)








# 2


Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is note: really looks like


Since 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


Also, because the slope is , this means:




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

So this is the graph of through the points and
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