SOLUTION: Graph the equations. (1) y = -x squared + 3x (2) y = x squared + 1

Question 122813: Graph the equations.
(1) y = -x squared + 3x
(2) y = x squared + 1
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 -2 to the 2nd power to get 4

Multiply -1 and 4 to get -4

Multiply 3 and -2 to get -6

Add -4 and -6 to get -10

So when , we have

So our 1st point is (-2,-10)

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

Multiply 3 and -1 to get -3

Add -1 and -3 to get -4

So when , we have

So our 2nd point is (-1,-4)

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

Multiply 3 and 0 to get 0

Add 0 and 0 to get 0

So when , we have

So our 3rd point is (0,0)

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

Multiply 3 and 1 to get 3

Add -1 and 3 to get 2

So when , we have

So our 4th point is (1,2)

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

Multiply 3 and 2 to get 6

Add -4 and 6 to get 2

So when , we have

So our 5th point is (2,2)

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

Multiply 3 and 3 to get 9

Add -9 and 9 to get 0

So when , we have

So our 6th point is (3,0)

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

Start with the given function

Plug in

Raise 4 to the 2nd power to get 16

Multiply -1 and 16 to get -16

Multiply 3 and 4 to get 12

Add -16 and 12 to get -4

So when , we have

So our 7th point is (4,-4)

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

Start with the given function

Plug in

Raise 5 to the 2nd power to get 25

Multiply -1 and 25 to get -25

Multiply 3 and 5 to get 15

Add -25 and 15 to get -10

So when , we have

So our 8th point is (5,-10)

Now lets make a table of the values we have calculated

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

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 10

So when , we have

So our 1st point is (-3,10)

-------------- 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 5

So when , we have

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

-------------- 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 2

So when , we have

So our 3rd point is (-1,2)

-------------- 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 2

So when , we have

So our 5th point is (1,2)

-------------- 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 5

So when , we have

So our 6th point is (2,5)

-------------- 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 10

So when , we have

So our 7th point is (3,10)

Now lets make a table of the values we have calculated

Now plot the points

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

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