Build a table of values relating y to x. You must take into account that what we really have is y=+-sqrt(2x+3). Plot the points and draw the best line you can through those points.
Note that the x-intercept is where y=0=sqrt(2x+3)
Also note that sqrt(0)=0" "=>" "2x+3=0
2x=-3
x_("intercept")=-3/2
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Lets suppose you do not have a calculator. Then you need to select values for 2x+3 that are known squared values and adjust x to give them.
This is the selection:
(+-1)^2=1
(+-2)^2=4
(+-3)^2=9
(+-4)^2=16
(+-5)^2=25 larr stop at this one as they are getting a bit big
color(blue)("Set "2x+3=1" " =>" " 2x=-2" " =>" "x=-1)
" "+-y=+-1=+-sqrt(2(-1)+3)
" "color(brown)(=> (x,y) = (-1,+1)" " &" " (-1,-1))
................................................................................................
color(blue)("Set "2x+3=4" " =>" " 2x=+1" " =>" "x=+1/2)
" "+-y=+-2=+-sqrt(2(1/2)+3)
" "color(brown)(=> (x,y) = (1/2,+2)" " &" " (1/2,-2))
................................................................................................
color(blue)("Set "2x+3=9" " =>" " 2x=+6" " =>" "x=+6/2
" "+-y=+-3=+-sqrt(2(6/2)+3)
" "color(brown)(=> (x,y) = (6/2,+3)" " &" " (6/2,-3))
................................................................................................
color(blue)("Set "2x+3=16" " =>" " 2x=+13" " =>" "x=+13/2
" "+-y=+-4=+-sqrt(2(13/2)+3)
" "color(brown)(=> (x,y) = (13/2,+4)" " &" " (13/2,-4))
................................................................................................
color(blue)("Set "2x+3=25" " =>" " 2x=+22" " =>" "x=+22/2
" "+-y=+-5=+-sqrt(2(22/2)+3)
" "color(brown)(=> (x,y) = (22/2,+5)" " &" " (22/2,-5))
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Your graph should look like this:
![Tony B]()
