what is x^2+y-4=0 symmetric to?

label Calculus
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x axis , y axis , origin? all or none ?

Oct 22nd, 2017

first solve for y

x^2+y-4=0    +4 to both sides          x^2+y-4+4=0+4 

x^2+y=4        -x^2 to both sides this will isolate y to graph          x^2-x^2+y=4-x^2

y=4-x^2    or      y=-x^2+4       now you can look at the graphing portion

you know that it will intercept the y axis at (0,4) because you have a +4 at the end

the slope is -1/1   because of the -1 in front of the x

now you can do a t chart to see what it will look like...   pick three numbers I like to choose a -#, 0 , +#

so for ex.    -2,0,2

-2 in our equation =    -(-2)^2+4 use order of operations

(-2)^2 = (-2)(-2)=  4

  -(4)+4   =   0                    order pair= (-2,0)

we already know 0            order pair  = (0,4)

now the last is 2 so

-(2)^2+4      2^2= 2*2=4


order pair = (2,0)

so from these when you graph you can see that it will be an upside down u and that the center will be the y axis so your line of symmetry or the point where you have equal halfs is the y axis

if you want I will have a worksheet put up in the next 24 hrs with help with this topic and practice problems. If you need it sooner send me a message and let me know

Sep 25th, 2014

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