Question 86559
 In order to graph {{{y=x^2-5x+11}}}, we need to plot some points. 
 So we can start at any x value. So lets start at x=-5 
 

{{{y=x^2-5x+11}}} Start with the given equation 
 
{{{y=(-5)^2-5(-5)+11}}} Plug in {{{x=-5}}} 
 
{{{(-5)^2-5(-5)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(-4)^2-5(-4)+11}}} Plug in {{{x=-4}}} 
 
{{{(-4)^2-5(-4)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(-3)^2-5(-3)+11}}} Plug in {{{x=-3}}} 
 
{{{(-3)^2-5(-3)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(-2)^2-5(-2)+11}}} Plug in {{{x=-2}}} 
 
{{{(-2)^2-5(-2)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(-1)^2-5(-1)+11}}} Plug in {{{x=-1}}} 
 
{{{(-1)^2-5(-1)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(0)^2-5(0)+11}}} Plug in {{{x=0}}} 
 
{{{(0)^2-5(0)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(1)^2-5(1)+11}}} Plug in {{{x=1}}} 
 
{{{(1)^2-5(1)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(2)^2-5(2)+11}}} Plug in {{{x=2}}} 
 
{{{(2)^2-5(2)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(3)^2-5(3)+11}}} Plug in {{{x=3}}} 
 
{{{(3)^2-5(3)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(4)^2-5(4)+11}}} Plug in {{{x=4}}} 
 
{{{(4)^2-5(4)+11=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^2-5x+11}}} Start with the given equation 
 
{{{y=(5)^2-5(5)+11}}} Plug in {{{x=5}}} 
 
{{{(5)^2-5(5)+11=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

<pre>
<TABLE width=500>

<TR><TD> x</TD><TD>y</TD></TR>

<TR><TD> -5</TD><TD>61</TD></TR> 
<TR><TD> -4</TD><TD>47</TD></TR> 
<TR><TD> -3</TD><TD>35</TD></TR> 
<TR><TD> -2</TD><TD>25</TD></TR> 
<TR><TD> -1</TD><TD>17</TD></TR> 
<TR><TD> 0</TD><TD>11</TD></TR> 
<TR><TD> 1</TD><TD>7</TD></TR> 
<TR><TD> 2</TD><TD>5</TD></TR> 
<TR><TD> 3</TD><TD>5</TD></TR> 
<TR><TD> 4</TD><TD>7</TD></TR> 
<TR><TD> 5</TD><TD>11</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing( 900, 900, -10, 10, -10, 10,
  grid( 1 ),circle(-5,61,0.05), 
  circle(-5,61,0.08), 
circle(-4,47,0.05), 
  circle(-4,47,0.08), 
circle(-3,35,0.05), 
  circle(-3,35,0.08), 
circle(-2,25,0.05), 
  circle(-2,25,0.08), 
circle(-1,17,0.05), 
  circle(-1,17,0.08), 
circle(0,11,0.05), 
  circle(0,11,0.08), 
circle(1,7,0.05), 
  circle(1,7,0.08), 
circle(2,5,0.05), 
  circle(2,5,0.08), 
circle(3,5,0.05), 
  circle(3,5,0.08), 
circle(4,7,0.05), 
  circle(4,7,0.08), 
circle(5,11,0.05), 
  circle(5,11,0.08) 
)}}}

Now connect the points, this is the graph of {{{y=x^2-5x+11}}}

{{{drawing( 900, 900, -10, 10, -10, 10,
  grid( 1 ),
  graph( 900, 900,-10, 10, -10, 10, x^2-5x+11),circle(-5,61,0.05), 
  circle(-5,61,0.08), 
circle(-4,47,0.05), 
  circle(-4,47,0.08), 
circle(-3,35,0.05), 
  circle(-3,35,0.08), 
circle(-2,25,0.05), 
  circle(-2,25,0.08), 
circle(-1,17,0.05), 
  circle(-1,17,0.08), 
circle(0,11,0.05), 
  circle(0,11,0.08), 
circle(1,7,0.05), 
  circle(1,7,0.08), 
circle(2,5,0.05), 
  circle(2,5,0.08), 
circle(3,5,0.05), 
  circle(3,5,0.08), 
circle(4,7,0.05), 
  circle(4,7,0.08), 
circle(5,11,0.05), 
  circle(5,11,0.08) 
)}}}


So by looking at the table, we can see that {{{f(-3)=35}}}. You were close. I'm assuming you calculated


{{{-3^2-5*-3+11=-9+15+11=17}}}you 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)


{{{(-3)^2-5*-3+11=9+15+11=35}}}