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

1 Answer
Dec 18, 2017

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]}