Questions on Geometry: Angles, complementary, supplementary angles answered by real tutors!

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Question 147611: Graph y=x2-2x-2
NOTE-the two after the first x is an exponent: Graph y=x2-2x-2
NOTE-the two after the first x is an exponent
Answer by jim_thompson5910(9926) About Me  (Show Source):
You can put this solution on YOUR website!

Table of Contents:


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In order to graph y=x^2-2x-2, we need to plot some points.


Let's find y when x=-2:


y=x^2-2x-2 Start with the given equation.


y=(-2)^2-2(-2)-2 Plug in x=-2.


y=1(4)-2(-2)-2 Square -2 to get 4.


y=4-2(-2)-2 Multiply 1 and 4 to get 4.


y=4+4-2 Multiply -2 and -2 to get 4.


y=6 Combine like terms.


So if x=-2, then y=6.


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Let's find y when x=-1:


y=x^2-2x-2 Start with the given equation.


y=(-1)^2-2(-1)-2 Plug in x=-1.


y=1(1)-2(-1)-2 Square -1 to get 1.


y=1-2(-1)-2 Multiply 1 and 1 to get 1.


y=1+2-2 Multiply -2 and -1 to get 2.


y=1 Combine like terms.


So if x=-1, then y=1.


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Let's find y when x=0
(Note: you can start with any x-value):


y=x^2-2x-2 Start with the given equation.


y=(0)^2-2(0)-2 Plug in x=0.


y=1(0)-2(0)-2 Square 0 to get 0.


y=0-2(0)-2 Multiply 1 and 0 to get 0.


y=0+0-2 Multiply -2 and 0 to get 0.


y=-2 Combine like terms.


So if x=0, then y=-2.


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Let's find y when x=1:


y=x^2-2x-2 Start with the given equation.


y=(1)^2-2(1)-2 Plug in x=1.


y=1(1)-2(1)-2 Square 1 to get 1.


y=1-2(1)-2 Multiply 1 and 1 to get 1.


y=1-2-2 Multiply -2 and 1 to get -2.


y=-3 Combine like terms.


So if x=1, then y=-3.


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Let's find y when x=2:


y=x^2-2x-2 Start with the given equation.


y=(2)^2-2(2)-2 Plug in x=2.


y=1(4)-2(2)-2 Square 2 to get 4.


y=4-2(2)-2 Multiply 1 and 4 to get 4.


y=4-4-2 Multiply -2 and 2 to get -4.


y=-2 Combine like terms.


So if x=2, then y=-2.


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Let's find y when x=3:


y=x^2-2x-2 Start with the given equation.


y=(3)^2-2(3)-2 Plug in x=3.


y=1(9)-2(3)-2 Square 3 to get 9.


y=9-2(3)-2 Multiply 1 and 9 to get 9.


y=9-6-2 Multiply -2 and 3 to get -6.


y=1 Combine like terms.


So if x=3, then y=1.


Let's find y when x=4:


y=x^2-2x-2 Start with the given equation.


y=(4)^2-2(4)-2 Plug in x=4.


y=1(16)-2(4)-2 Square 4 to get 16.


y=16-2(4)-2 Multiply 1 and 16 to get 16.


y=16-8-2 Multiply -2 and 4 to get -8.


y=6 Combine like terms.


So if x=4, then y=6.


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Now let's make a table of the values we just found.


Table of Values:





xy
-26


-11


0-2


1-3


2-2


31


46

Now let's plot the points:


drawing(900, 900, -10, 10, -10, 10,<BR> grid(1),<BR> graph(900, 900, -10, 10, -10, 10, 0),<BR> circle(-2,6,0.08),circle(-2,6,0.10),<BR> circle(-1,1,0.08),circle(-1,1,0.10),<BR> circle(0,-2,0.08),circle(0,-2,0.10),<BR> circle(1,-3,0.08),circle(1,-3,0.10),<BR> circle(2,-2,0.08),circle(2,-2,0.10),<BR> circle(3,1,0.08),circle(3,1,0.10),<BR> circle(4,6,0.08),circle(4,6,0.10) <BR> )




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Now draw a curve through all of the points to graph y=x^2-2x-2:


drawing(900, 900, -10, 10, -10, 10,<BR> grid(1),<BR> graph(900, 900, -10, 10, -10, 10, x^2-2x-2),<BR> circle(-2,6,0.08),circle(-2,6,0.10),<BR> circle(-1,1,0.08),circle(-1,1,0.10),<BR> circle(0,-2,0.08),circle(0,-2,0.10),<BR> circle(1,-3,0.08),circle(1,-3,0.10),<BR> circle(2,-2,0.08),circle(2,-2,0.10),<BR> circle(3,1,0.08),circle(3,1,0.10),<BR> circle(4,6,0.08),circle(4,6,0.10) <BR> ) Graph of y=x^2-2x-2