Question 83761
To graph {{{y=(x-7)^2+5}}} simply choose a set of x values and plug them in to find the y values. After that, you can plot the points and graph the equation


{{{y=(x-7)^2+5}}} Start with the given equation 
 
{{{y=((4)-7)^2+5}}} Plug in {{{x=4}}} 
 
{{{((4)-7)^2+5=14}}} Calculate the y value

So when {{{x=4}}} {{{y=14}}}

So our 1st point is (4,14)




 

{{{y=(x-7)^2+5}}} Start with the given equation 
 
{{{y=((5)-7)^2+5}}} Plug in {{{x=5}}} 
 
{{{((5)-7)^2+5=9}}} Calculate the y value

So when {{{x=5}}} {{{y=9}}}

So our 2nd point is (5,9)




 

{{{y=(x-7)^2+5}}} Start with the given equation 
 
{{{y=((6)-7)^2+5}}} Plug in {{{x=6}}} 
 
{{{((6)-7)^2+5=6}}} Calculate the y value

So when {{{x=6}}} {{{y=6}}}

So our 3rd point is (6,6)




 

{{{y=(x-7)^2+5}}} Start with the given equation 
 
{{{y=((7)-7)^2+5}}} Plug in {{{x=7}}} 
 
{{{((7)-7)^2+5=5}}} Calculate the y value

So when {{{x=7}}} {{{y=5}}}

So our 4th point is (7,5)




 

{{{y=(x-7)^2+5}}} Start with the given equation 
 
{{{y=((8)-7)^2+5}}} Plug in {{{x=8}}} 
 
{{{((8)-7)^2+5=6}}} Calculate the y value

So when {{{x=8}}} {{{y=6}}}

So our 5th point is (8,6)




 

{{{y=(x-7)^2+5}}} Start with the given equation 
 
{{{y=((9)-7)^2+5}}} Plug in {{{x=9}}} 
 
{{{((9)-7)^2+5=9}}} Calculate the y value

So when {{{x=9}}} {{{y=9}}}

So our 6th point is (9,9)




 

{{{y=(x-7)^2+5}}} Start with the given equation 
 
{{{y=((10)-7)^2+5}}} Plug in {{{x=10}}} 
 
{{{((10)-7)^2+5=14}}} Calculate the y value

So when {{{x=10}}} {{{y=14}}}

So our 7th point is (10,14)




 



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> 4</TD><TD>14</TD></TR> 
<TR><TD> 5</TD><TD>9</TD></TR> 
<TR><TD> 6</TD><TD>6</TD></TR> 
<TR><TD> 7</TD><TD>5</TD></TR> 
<TR><TD> 8</TD><TD>6</TD></TR> 
<TR><TD> 9</TD><TD>9</TD></TR> 
<TR><TD> 10</TD><TD>14</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing( 900, 900, -5,15,-5,15,
  grid( 1 ),circle(4,14,0.05), 
  circle(4,14,0.08), 
circle(5,9,0.05), 
  circle(5,9,0.08), 
circle(6,6,0.05), 
  circle(6,6,0.08), 
circle(7,5,0.05), 
  circle(7,5,0.08), 
circle(8,6,0.05), 
  circle(8,6,0.08), 
circle(9,9,0.05), 
  circle(9,9,0.08), 
circle(10,14,0.05), 
  circle(10,14,0.08) 
)}}}



Now connect the points, this is the graph of (x-7)^2+5



{{{drawing( 900, 900, -5,15,-5,15,
  grid( 1 ),
  graph( 900, 900,-5,15,-5,15, (x-7)^2+5),circle(4,14,0.05), 
  circle(4,14,0.08), 
circle(5,9,0.05), 
  circle(5,9,0.08), 
circle(6,6,0.05), 
  circle(6,6,0.08), 
circle(7,5,0.05), 
  circle(7,5,0.08), 
circle(8,6,0.05), 
  circle(8,6,0.08), 
circle(9,9,0.05), 
  circle(9,9,0.08), 
circle(10,14,0.05), 
  circle(10,14,0.08) 
)}}}