Question

How do you find the vertex of `f(x)=3(x+4)^2+2`?

Answer 1

Compare with the general vertex form to get that the vertex is at `(-4, 2)`.

Explanation:

That function, `f(x) = 3(x + 4)^2 + 2` is already in the vertex form, `f(x) = a(x - h) + k`.

We could then see that `k`, the `y`-coordinate of the vertex, is `2`. However, for the `x`-coordinate, in the vertex form it should be subtracted, but in our function it is added.

No worries! Since two subtractions "combine" into an addition, we could reverse this process:

`f(x) = 3(x + 4)^2 + 2 rarr f(x) = 3(x - (- 4))^2 + 2`

Now we can compare with the vertex form to see that `h`, the `x`-coordinate of the vertex, is at `-4`.

To conclude, the vertex is at `(-4, 2)`. Here's what the graph looks like:

graph{y=3(x+4)^2+2 [-10, 10, -5, 5]}