+0  
 
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avatar+48 

The graph above is the graph of y=x2 translated and reflected in the xy-plane. Find an equation for this graph.

Please help

 Feb 19, 2019
 #1
avatar+98126 
+3

y = x^2    has the vertex at (0, 0)

 

So....we have

 

y = (x - 0)^2 + 0

 

This graph translates the vertex to the left 7 units and up 4 units

 

So...we have

 

y = ( x + 0 + 7) ^2 + ( 0 + 4 ) 

 

y = ( x + 7)^2 + 4

 

 

cool cool cool

 Feb 19, 2019
 #2
avatar+48 
+2

Thanks for the answer! I have a question though. Shifting it to the left makes it -7, so how does it turn positive?

Roxettna  Feb 19, 2019
 #3
avatar+98126 
+4

This is always confusing....

 

Note that  we have

 

(x + 7)^2 + 4

 

The form that we are really going for is

 

( x - h)^2 + k        where ( h, k) is the vertex

 

So....

 

(x - (-7) )^2 + 4     produces the vertex (h, k)  =  (-7, 4)

 

But this is just the same as

 

(x + 7)^2 + 4

 

Remember that a " + "  moves the x coordinate of the vertex to the left  and a " - "  moves the x coordinate of the vertex to the right

 

To get a feel for this....look at the graph here :  https://www.desmos.com/calculator/4ryl8slhym

 

y = ( x + 2)^2  shifts the vertex of y = x^2 to the left 2 units

 

y = ( x - 2)^2  shifts the vertex of y = x^2 to the right by 2 units

 

 

cool cool cool

CPhill  Feb 19, 2019
 #4
avatar+48 
+1

You're responses are so thorough! Thank you so much for taking the time to explain it in detail, I really appreciate it. It's a whole lot clearer to me now

Roxettna  Feb 19, 2019
 #5
avatar+98126 
+1

OK....glad to help....

 

 

cool cool cool

CPhill  Feb 19, 2019

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