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

Please help

Roxettna Feb 19, 2019

#1**+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

CPhill Feb 19, 2019

#2**+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**+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

CPhill
Feb 19, 2019