SOLUTION: Hi thank you Cecilia, for the solution to my other problem, Here is another one I am not sure of: Use several points to graph. If f(x)= xsquared - 5x + 11. Find f(-3).

Algebra ->  Graphs -> SOLUTION: Hi thank you Cecilia, for the solution to my other problem, Here is another one I am not sure of: Use several points to graph. If f(x)= xsquared - 5x + 11. Find f(-3).       Log On


   

Question 86559: Hi thank
you Cecilia, for the solution to my other problem, Here is another one I am not sure of: Use several points to graph. If f(x)= xsquared - 5x + 11. Find f(-3). I have an answer of 17, but am not sure. Thank you for your much needed help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph y=x%5E2-5x%2B11, we need to plot some points.
So we can start at any x value. So lets start at x=-5

y=x%5E2-5x%2B11 Start with the given equation

y=%28-5%29%5E2-5%28-5%29%2B11 Plug in x=-5

%28-5%29%5E2-5%28-5%29%2B11=61 Calculate the y value by following the order of operations
So when x=-5 y=61
So our 1st point is (-5,61)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%28-4%29%5E2-5%28-4%29%2B11 Plug in x=-4

%28-4%29%5E2-5%28-4%29%2B11=47 Calculate the y value by following the order of operations
So when x=-4 y=47
So our 2nd point is (-4,47)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%28-3%29%5E2-5%28-3%29%2B11 Plug in x=-3

%28-3%29%5E2-5%28-3%29%2B11=35 Calculate the y value by following the order of operations
So when x=-3 y=35
So our 3rd point is (-3,35)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%28-2%29%5E2-5%28-2%29%2B11 Plug in x=-2

%28-2%29%5E2-5%28-2%29%2B11=25 Calculate the y value by following the order of operations
So when x=-2 y=25
So our 4th point is (-2,25)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%28-1%29%5E2-5%28-1%29%2B11 Plug in x=-1

%28-1%29%5E2-5%28-1%29%2B11=17 Calculate the y value by following the order of operations
So when x=-1 y=17
So our 5th point is (-1,17)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%280%29%5E2-5%280%29%2B11 Plug in x=0

%280%29%5E2-5%280%29%2B11=11 Calculate the y value by following the order of operations
So when x=0 y=11
So our 6th point is (0,11)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%281%29%5E2-5%281%29%2B11 Plug in x=1

%281%29%5E2-5%281%29%2B11=7 Calculate the y value by following the order of operations
So when x=1 y=7
So our 7th point is (1,7)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%282%29%5E2-5%282%29%2B11 Plug in x=2

%282%29%5E2-5%282%29%2B11=5 Calculate the y value by following the order of operations
So when x=2 y=5
So our 8th point is (2,5)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%283%29%5E2-5%283%29%2B11 Plug in x=3

%283%29%5E2-5%283%29%2B11=5 Calculate the y value by following the order of operations
So when x=3 y=5
So our 9th point is (3,5)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%284%29%5E2-5%284%29%2B11 Plug in x=4

%284%29%5E2-5%284%29%2B11=7 Calculate the y value by following the order of operations
So when x=4 y=7
So our 10th point is (4,7)




Now lets find another point
y=x%5E2-5x%2B11 Start with the given equation

y=%285%29%5E2-5%285%29%2B11 Plug in x=5

%285%29%5E2-5%285%29%2B11=11 Calculate the y value by following the order of operations
So when x=5 y=11
So our 11th point is (5,11)






Now lets make a table of the values we have calculated 



 xy



 -561
 

 -447
 

 -335
 

 -225
 

 -117
 

 011
 

 17
 

 25
 

 35
 

 47
 

 511
Now plot the points

Now connect the points, this is the graph of y=x%5E2-5x%2B11


So by looking at the table, we can see that f%28-3%29=35. You were close. I'm assuming you calculated

-3%5E2-5%2A-3%2B11=-9%2B15%2B11=17you only squared the 3 and not the negative

where you should have done this (note: I'm squaring the negative also. So it goes from -3 to 9)

%28-3%29%5E2-5%2A-3%2B11=9%2B15%2B11=35