SOLUTION: Can you please help me graph this equation? y=-x^2+6x+5

Question 128757: Can you please help me graph this equation?
y=-x^2+6x+5
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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 6 and -2 to get -12

Add -4 and -12 to get -16

Add -16 and 5 to get -11

So when , we have

So our 1st point is (-2,-11)

-------------- 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 6 and -1 to get -6

Add -1 and -6 to get -7

Add -7 and 5 to get -2

So when , we have

So our 2nd 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

Multiply 6 and 0 to get 0

Add 0 and 0 to get 0

Add 0 and 5 to get 5

So when , we have

So our 3rd point is (0,5)

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

Multiply 6 and 1 to get 6

Add -1 and 6 to get 5

Add 5 and 5 to get 10

So when , we have

So our 4th point is (1,10)

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

Multiply 6 and 2 to get 12

Add -4 and 12 to get 8

Add 8 and 5 to get 13

So when , we have

So our 5th point is (2,13)

-------------- 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 6 and 3 to get 18

Add -9 and 18 to get 9

Add 9 and 5 to get 14

So when , we have

So our 6th point is (3,14)

-------------- 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 6 and 4 to get 24

Add -16 and 24 to get 8

Add 8 and 5 to get 13

So when , we have

So our 7th point is (4,13)

-------------- 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 6 and 5 to get 30

Add -25 and 30 to get 5

Add 5 and 5 to get 10

So when , we have

So our 8th point is (5,10)

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

Start with the given function

Plug in

Raise 6 to the 2nd power to get 36

Multiply -1 and 36 to get -36

Multiply 6 and 6 to get 36

Add -36 and 36 to get 0

Add 0 and 5 to get 5

So when , we have

So our 9th point is (6,5)

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

Start with the given function

Plug in

Raise 7 to the 2nd power to get 49

Multiply -1 and 49 to get -49

Multiply 6 and 7 to get 42

Add -49 and 42 to get -7

Add -7 and 5 to get -2

So when , we have

So our 10th point is (7,-2)

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

Start with the given function

Plug in

Raise 8 to the 2nd power to get 64

Multiply -1 and 64 to get -64

Multiply 6 and 8 to get 48

Add -64 and 48 to get -16

Add -16 and 5 to get -11

So when , we have

So our 11th point is (8,-11)

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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