Question

How do you sketch the graph of `y=1/5x^2-4` and describe the transformation?

Answer 1

See Explanation

Explanation:

First what you have to do is find out what the base equation is. In this case, it is `y=x^2`. graph{x^2 [-10, 10, -5, 5]}
If you know what this graph looks like then the process is much easier, but you can also take the time to write out some points to give yourself an idea of its shape.

When you multiply the `x^2` portion of the parabola, you perform what is called a vertical compression by a factor of 5 or a horizontal stretch by a factor of 5. This might sound scary but what it really does is squeeze the graph so it is not as steep. graph{1/5x^2 [-10, 10, -5, 5]}
The -4 operation is just a vertical translation down 4 units, so the center (vertex) of the parabola is (0,-4). This operation just simply moves the graph up or down the y axis (vertical).
graph{1/5x^2-4 [-10, 10, -5, 5]}