Question 90405
Lets find the value of y when  {{{x=-4}}}


{{{y=x^2+2x-3}}} Start with the given polynomial



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



{{{y=(16)+2(-4)-3}}} Raise -4 to the second power to get 16



{{{y=(16)+-8-3}}} Multiply 2 by -4 to get -8



{{{y=5}}} Now combine like terms

So when {{{x=-4}}}, {{{y=5}}}




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




Lets find the value of y when  {{{x=-3}}}


{{{y=x^2+2x-3}}} Start with the given polynomial



{{{y=(-3)^2+2(-3)-3}}} Plug in {{{x=-3}}}



{{{y=(9)+2(-3)-3}}} Raise -3 to the second power to get 9



{{{y=(9)+-6-3}}} Multiply 2 by -3 to get -6



{{{y=0}}} Now combine like terms

So when {{{x=-3}}}, {{{y=0}}}




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




Lets find the value of y when  {{{x=-2}}}


{{{y=x^2+2x-3}}} Start with the given polynomial



{{{y=(-2)^2+2(-2)-3}}} Plug in {{{x=-2}}}



{{{y=(4)+2(-2)-3}}} Raise -2 to the second power to get 4



{{{y=(4)+-4-3}}} Multiply 2 by -2 to get -4



{{{y=-3}}} Now combine like terms

So when {{{x=-2}}}, {{{y=-3}}}




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




Lets find the value of y when  {{{x=-1}}}


{{{y=x^2+2x-3}}} Start with the given polynomial



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



{{{y=(1)+2(-1)-3}}} Raise -1 to the second power to get 1



{{{y=(1)+-2-3}}} Multiply 2 by -1 to get -2



{{{y=-4}}} Now combine like terms

So when {{{x=-1}}}, {{{y=-4}}}




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




Lets find the value of y when  {{{x=0}}}


{{{y=x^2+2x-3}}} Start with the given polynomial



{{{y=(0)^2+2(0)-3}}} Plug in {{{x=0}}}



{{{y=(0)+2(0)-3}}} Raise 0 to the second power to get 0



{{{y=(0)+0-3}}} Multiply 2 by 0 to get 0



{{{y=3}}} Remove any zero terms

So when {{{x=0}}}, {{{y=-3}}}




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




Lets find the value of y when  {{{x=1}}}


{{{y=x^2+2x-3}}} Start with the given polynomial



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



{{{y=(1)+2(1)-3}}} Raise 1 to the second power to get 1



{{{y=(1)+2-3}}} Multiply 2 by 1 to get 2



{{{y=0}}} Now combine like terms

So when {{{x=1}}}, {{{y=0}}}




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




Lets find the value of y when  {{{x=2}}}


{{{y=x^2+2x-3}}} Start with the given polynomial



{{{y=(2)^2+2(2)-3}}} Plug in {{{x=2}}}



{{{y=(4)+2(2)-3}}} Raise 2 to the second power to get 4



{{{y=(4)+4-3}}} Multiply 2 by 2 to get 4



{{{y=5}}} Now combine like terms

So when {{{x=2}}}, {{{y=5}}}



Now lets make a table 



<pre>
<TABLE width=500>

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

<TR><TD> -4</TD><TD>5</TD></TR> 
<TR><TD> -3</TD><TD>0</TD></TR> 
<TR><TD> -2</TD><TD>-3</TD></TR> 
<TR><TD> -1</TD><TD>-4</TD></TR> 
<TR><TD> 0</TD><TD>-3</TD></TR> 
<TR><TD> 1</TD><TD>0</TD></TR> 
<TR><TD> 2</TD><TD>5</TD></TR> 
</TABLE>
</pre>



Notice if we graph {{{x^2+2x-3}}} and plot the points we found earlier, we see that the points lie on the curve. So this verifies our answer.

{{{drawing(900,900,-10,10,-10,10,
grid( 1 ),
graph(900,900,-10,10,-10,10, x^2+2x-3),circle(-4,5,0.05),
circle(-4,5,0.08),
circle(-3,0,0.05),
circle(-3,0,0.08),
circle(-2,-3,0.05),
circle(-2,-3,0.08),
circle(-1,-4,0.05),
circle(-1,-4,0.08),
circle(0,-3,0.05),
circle(0,-3,0.08),
circle(1,0,0.05),
circle(1,0,0.08),
circle(2,5,0.05),
circle(2,5,0.08),
circle(3,12,0.05),
circle(3,12,0.08))}}}