Which function represents a translation of the graph of y=x^2 by 10 units to the left?

Question

1. Which function represents a translation of the graph of y=x^2 by 10 units to the left?
Y=x^2+10
Y=10x^2
Y=(x-10)^2
Y=(x+10)^2

2. In the function y=1/3x^2, what effect does the number 1/3 have on the graph, as compared to the graph of the function y=x^2?
(Points : 3)
It stretches the graph vertically by a factor of 3.
It shrinks the graph vertically to 1/3 its original height.
It stretches the graph horizontally by a factor of 3.
It shrinks the graph horizontally to 1/3 its original width.

Answer 1

Christy, your equation is y = (x-h)² + k, where (h,k) is your vertex.

 

Since a "normal" parabola has its vertex at (0,0), we have y = a(x-0)² + 0 = ax²

 

1. Remembering that h is your x coordinate, our new x coordinate is -10, because we went from 0 left 10 to -10.

Therefore, our equation is y = (x-(10))² = (x + 10)², so your answer is the last.

 

2. This does the opposite of what you would think.  It stretches the graph horizontally by a factor of 3.  If you had y = 3x², it would shrink it horizontally by 1/3.

 

Hope this helps!