Question

What is the vertex of the parabola `y=-x^2-2x+3`?

Answer 1

`(-1,4)`

Explanation:

There is a lovely and straightforward (which makes it all the lovelier) rule for working out vertices such as this one.

Think of the general parabola: `y=ax^2+bx+c`, where `a!=0`

The formula for finding the `x`-vertex is `(-b)/(2a)` and to find the `y`-vertex, you insert the value you found for `x` into the formula.

Using your question `y=-x^2-2x+3` we can establish the values of `a, b,`and `c`.

In this case:

`a=-1`
`b=-2`; and
`c=3`.

To find the `x`-vertex we need to replace the values for `a` and `b` in the formula given above (`color(red)((-b)/(2a))`):

`=(-(-2))/(2*(-1))=2/(-2)=-1`

So we now know that the `x`-vertex is at `-1`.

To find the `y`-vertex, go back to the original question and replace all the instances of `x` with `-1`:

`y=-x^2-2x+3`

`y=-(-1)^2-2*(-1)+3`

`y=-1+2+3`

`y=4`

We now know that the `x`-vertex is at `-1` and the `y`-vertex is at `4` and this can be written in coordinate format:

`(-1,4)`