In which quadrant would the vertex of f(x+ 3) + 2 be located?

I'm thinking that this is supposed to be a quadratic and you forgot the ^2 at the end of the (x + 3). IF this is the case, then the vertex form of a quadratic is

[tex]y=(x-h)^2+k[/tex] where the h inside the parenthesis with the x- indicates side to side movement and the k indicates up and down movement. Both translations begin at the origin, of course. The important thing to remember here is that the form "x -" is constant. So if our quadratic reflects "x - 3", then it is understood to be "x - (3)" and the movement is 3 units to the right. If the quadratic reflects "x + 3", then it is understood to be "x - (-3)" and the movement is 3 units to the left. Our quadratic, then, is shifted 3 units to the left of the origin and up 2 units, putting us in QII.

If this is what it appears to be, (x + 3) + 2, then it is x + 5 which is a line that has no vertex (which is why I'm thinking it must be a mistyped quadratic!)

MrRoyal MrRoyal · Answer 2 · 2022-04-12T10:58:35+02:00

The vertex of the function f(x + 3) + 2 is located in the second quadrant

How to determine the quadrant of the vertex?

Assume the function is a quadratic function represented as:

f(x) = x^2

The transformed function f(x + 3) + 2 would be:

f(x + 3) + 2 = (x + 3)^2 + 2

The vertex of the quadratic function is:

(h,k) = (-3,2)

The above point is located in the second quadrant.

Hence, the vertex is located in the second quadrant