Question

How do you use the important points to sketch the graph of `y = (x + 4)^2 - 3`?

Answer 1

The important points are
`(-3,-2)`;
`(-2,1)`;
`(-5,-2)`;
`(-6,1)`

Explanation:

For the parent function of a quadratic equation `y=x^2`, the important points are `(1,1)`; `(2,4)`; `(-1,1)`; `(-2,4)`.

This equation is similar to the parent function but has shifted on the `x` and `y` axis.

The `-3` is the y-intercept on the line and means there is a `3` unit shift downward for all the `y` coordinates.

There is also a `4` unit shift left on all the `x` coordinates.

Using these rules, the important points are
`(-3,-2)`;
`(-2,1)`;
`(-5,-2)`;
`(-6,1)`