Question 332279


In order to graph {{{y=4(x+5)^2-1}}}, we need to plot a few points.



To get points in the form of (x,y), we need to find corresponding 'y' values to given 'x' values.



Let's find the y value when {{{x=-7}}}



{{{y=4(x+5)^2-1}}} Start with the given equation.



{{{y=4(-7+5)^2-1}}} Plug in {{{x=-7}}}.



{{{y=4(-2)^2-1}}} Add -7 to 5 to get -2.



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



{{{y=16-1}}} Multiply 4 and 4 to get 16 .



{{{y=15}}} Subtract 1 from 16 to get 15 .



So if {{{x=-7}}}, then {{{y=15}}} which gives us the point (-7,15).



----------------------------



Let's find the y value when {{{x=-6}}}



{{{y=4(x+5)^2-1}}} Start with the given equation.



{{{y=4(-6+5)^2-1}}} Plug in {{{x=-6}}}.



{{{y=4(-1)^2-1}}} Add -6 to 5 to get -1.



{{{y=4(1)-1}}} Square -1 to get 1.



{{{y=4-1}}} Multiply 4 and 1 to get 4 .



{{{y=3}}} Subtract 1 from 4 to get 3 .



So if {{{x=-6}}}, then {{{y=3}}} which gives us the point (-6,3).



----------------------------



Let's find the y value when {{{x=-5}}}



{{{y=4(x+5)^2-1}}} Start with the given equation.



{{{y=4(-5+5)^2-1}}} Plug in {{{x=-5}}}.



{{{y=4(0)^2-1}}} Add -5 to 5 to get 0.



{{{y=4(0)-1}}} Square 0 to get 0.



{{{y=0-1}}} Multiply 4 and 0 to get 0 .



{{{y=-1}}} Subtract 1 from 0 to get -1 .



So if {{{x=-5}}}, then {{{y=-1}}} which gives us the point (-5,-1).



----------------------------



Let's find the y value when {{{x=-4}}}



{{{y=4(x+5)^2-1}}} Start with the given equation.



{{{y=4(-4+5)^2-1}}} Plug in {{{x=-4}}}.



{{{y=4(1)^2-1}}} Add -4 to 5 to get 1.



{{{y=4(1)-1}}} Square 1 to get 1.



{{{y=4-1}}} Multiply 4 and 1 to get 4 .



{{{y=3}}} Subtract 1 from 4 to get 3 .



So if {{{x=-4}}}, then {{{y=3}}} which gives us the point (-4,3).



----------------------------



Let's find the y value when {{{x=-3}}}



{{{y=4(x+5)^2-1}}} Start with the given equation.



{{{y=4(-3+5)^2-1}}} Plug in {{{x=-3}}}.



{{{y=4(2)^2-1}}} Add -3 to 5 to get 2.



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



{{{y=16-1}}} Multiply 4 and 4 to get 16 .



{{{y=15}}} Subtract 1 from 16 to get 15 .



So if {{{x=-3}}}, then {{{y=15}}} which gives us the point (-3,15).



----------------------------



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



<h4>Table of Values:</h4><pre>

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</TD></TR><tr><td>-7</td><td>15</td></tr>
<tr><td>-6</td><td>3</td></tr>
<tr><td>-5</td><td>-1</td></tr>
<tr><td>-4</td><td>3</td></tr>
<tr><td>-3</td><td>15</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(500, 500, -10, 10, -3, 18,
grid(1),
graph(500, 500, -10, 10, -3, 18, 0),
circle(-7,15,0.08),circle(-7,15,0.10),circle(-7,15,0.12),circle(-7,15,0.14),
circle(-6,3,0.08),circle(-6,3,0.10),circle(-6,3,0.12),circle(-6,3,0.14),
circle(-5,-1,0.08),circle(-5,-1,0.10),circle(-5,-1,0.12),circle(-5,-1,0.14),
circle(-4,3,0.08),circle(-4,3,0.10),circle(-4,3,0.12),circle(-4,3,0.14),
circle(-3,15,0.08),circle(-3,15,0.10),circle(-3,15,0.12),circle(-3,15,0.14)

)}}}


<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=4(x+5)^2-1}}}:



{{{ drawing(500, 500, -10, 10, -3, 18,
grid(1),
graph(500, 500, -10, 10, -3, 18, 4(x+5)^2-1),
circle(-7,15,0.08),circle(-7,15,0.10),circle(-7,15,0.12),circle(-7,15,0.14),
circle(-6,3,0.08),circle(-6,3,0.10),circle(-6,3,0.12),circle(-6,3,0.14),
circle(-5,-1,0.08),circle(-5,-1,0.10),circle(-5,-1,0.12),circle(-5,-1,0.14),
circle(-4,3,0.08),circle(-4,3,0.10),circle(-4,3,0.12),circle(-4,3,0.14),
circle(-3,15,0.08),circle(-3,15,0.10),circle(-3,15,0.12),circle(-3,15,0.14)

)}}} Graph of {{{y=4(x+5)^2-1}}}