reflection question: y = x^2 + 2 is reflected in y-axis

[khorven]

Which equation represents the image of y = x^2 + 2 after a reflection in the y-axis?

A. y = -x^2 - 2
B. y = x^2 + 2
C. y = -x^2 + 2
D. y = x^2 - 2

Is there any way to solve this without graphing it or using intuition, i.e. by using equations?

 

[Deleted member 4993]

Which equation represents the image of y = x^2 + 2 after a reflection in the y-axis?

A. y = -x^2 - 2
B. y = x^2 + 2
C. y = -x^2 + 2
D. y = x^2 - 2

Is there any way to solve this without graphing it or using intuition, i.e. by using equations?

What changes take place due to reflection?

 

[khorven]

The negative Xs become positive and visa versa.

 

[Ishuda]

The negative Xs become positive and visa versa.

So, in your equation, replace each x by -x, i.e.
y= x + 3
reflected about the y axis becomes
y = -x + 3
and
y = x²
becomes
y = (-x)²

 

[khorven]

So that leaves me with y = (-x)^2 + 2. Then what? Change it to y = x^2 + 2 because no square will be negative?

 

[Ishuda]

So that leaves me with y = (-x)^2 + 2. Then what? Change it to y = x^2 + 2 because no square will be negative?

Yes, change it because (-x)²=x²

 

[khorven]

Thanks, bro.