Question

How do you:
Describe how the graph of y= x2 can be transformed to the graph of the given equation.

y = x2 + 13

Answer 1

x^2

Answer 2

The general transformation of a quadratic is
\( y=a(x-h)^2+k \)
where h=horizontal translation to the right
k= vertical translation upwards
a=scaling factor.
Can you proceed from here?

Answer 3

So it would be k=13.
So it would shift UP 13 units? down right left....?

Answer 4

Yes, from y=x^2 to y=x^2+13, the graph is shifted upwards by 13 units by adding 13 to y.

Answer 5

Down would be k=-13
Right would have been h=13, and left would have been h=-13.