I need urgent help finding equation of a parabola!!

Question

The graph of j(x) is a horizontal stretch of the graph f(x)=x²  by a factor of 7. What is the equation of j(x)?

Answer 1

I read this question a bit differently than Michael J did.

A horizontal stretch means that we're monkeying with the x coordinate of the graph. So, whatever we're doing, it's inside the function that is being applied, not outside. So, that means we're doing something like this:

j(x) = (_x)²

The blank is going to be something we do to x, and it's inside the squared part, where x is.

 

The confusing part about monkeying with x is that, whatever we do to x, it has the opposite effect of what we'd intuitively think.  So, if we subtract 2 from x, it moves the graph 2 to the right, not left.  And if we multiply x by something, it actually shrinks the graph by that factor, not stretches it.

 

So, to stretch the graph horizontally by a factor of 7, we divide x by 7:

 

j(x) = (x/7)²

 

Let's try it for a point that we know is on the graph. 

 

- For the original f(x), when we plug in 2 for x, we get f(2) = 4 for y.  So that's (2,4).

- On a graph that is stretched horizontally by a factor of 7, we'd expect that point to move over to (2 x 7, 4), so that'd be (14,4).  If you calculate j(14) by plugging in 14 for x, you get 14/7 = 2, and then you square it, which gives you 4.  Chhhhheck.  :)

 

If you wanted to do something to the y coordinate of the graph, like stretch it or shrink it vertically, you'd do things outside of the function, so you'd multiply or divide x² by something.  But in this question, it asked for a horizontal change, so you have to do something to the x coordinate.

 

Hope this helps!

 

 

Answer 2

f(x) = x²

 

When you have a horizontal stretch, you divide the function by the factor. Therefore, the new equation is

 

j(x) = (1/7)x²

 

You can graph these two functions on a calculator to verify.