transformations - stretches equation?

Question

if (1,1) is on the graph of y=x^2, then what point must be on the graph y=0.5x^2?

this is all it said on my sheet.

the teacher did an example:

if (3,27) is on the graph of y=x^3 then what point must be on the graph y=2x^3?

the answer was: (3,54)

Answer 1

It looks like you're leaving out some information from the problem.

Finding points on y=0.5x^2 is easy enough. Just plug in your favorite x-values and see what the equation spits out for y.

When x = 0, y = 0
When x = 1, y = 0.5
When x = 2, y = 2
... and so on and so forth.

Answer 2

For y=x^2, y=1 and x=1
For y=0.5x^2, then you can graph all possibilities of x
e.g., if x=1 then y=0.5
x=2, y=1; y=0.5(2^2)
x=3, y=4.5; y=0.5(3^2)
x=4, y=8; y=0.5(4^2)
x=5, y=12.5; y=0.5(5^2)
x=6, y=18; y=0.5(6^2)

the () are not nessacery, however they make it easier to understand the order of operations.

Answer 3

Per your teacher's example, the answer is (1, 0.5), because the only difference between the two equations given is the multiplication by 0.5.

Answer 4

The first positive integer pair to satisfy your new equation is (2,2) (0.5*2^2 = 2) Is that what you're looking for?

Answer 5

There are lots of points on y = .5x^2.

You are probably looking for (1, .5)