SOLUTION: Sketch the graph of the following functions h(x) = -x^2 + 2

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Question 87018: Sketch the graph of the following functions
h(x) = -x^2 + 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph y=-x%5E2%2B2, we need to plot some points.
We can start at any x value, so lets start at x=-3

h%28x%29=-x%5E2%2B2 Start with the given polynomial
h%28-3%29=-%28-3%29%5E2%2B2 Plug in x=-3

h%28-3%29=-7 Evaluate the expression by following the order of operations

So our first point is (-3,-7)




----Now lets find another point----



h%28x%29=-x%5E2%2B2 Start with the given polynomial
h%28-2%29=-%28-2%29%5E2%2B2 Plug in x=-2

h%28-2%29=-2 Evaluate the expression by following the order of operations

So our second point is (-2,-2)




----Now lets find another point----



h%28x%29=-x%5E2%2B2 Start with the given polynomial
h%28-1%29=-%28-1%29%5E2%2B2 Plug in x=-1

h%28-1%29=1 Evaluate the expression by following the order of operations

So our third point is (-1,1)




----Now lets find another point----



h%28x%29=-x%5E2%2B2 Start with the given polynomial
h%280%29=-%280%29%5E2%2B2 Plug in x=0

h%280%29=2 Evaluate the expression by following the order of operations

So our fourth point is (0,2)




----Now lets find another point----



h%28x%29=-x%5E2%2B2 Start with the given polynomial
h%281%29=-%281%29%5E2%2B2 Plug in x=1

h%281%29=1 Evaluate the expression by following the order of operations

So our fifth point is (1,1)




----Now lets find another point----



h%28x%29=-x%5E2%2B2 Start with the given polynomial
h%282%29=-%282%29%5E2%2B2 Plug in x=2

h%282%29=-2 Evaluate the expression by following the order of operations

So our sixth point is (2,-2)




----Now lets find another point----



h%28x%29=-x%5E2%2B2 Start with the given polynomial
h%283%29=-%283%29%5E2%2B2 Plug in x=3

h%283%29=-7 Evaluate the expression by following the order of operations

So our seventh point is (3,-7)




----Now lets find another point----



Now lets make a table of the values we have calculated 



 xy



 -3-7
 

 -2-2
 

 -11
 

 02
 

 11
 

 2-2
 

 3-7
Now plot the points



Now connect the points to graph y=-x%5E2%2B2