Question

Which of the following equations is of a parabola with a vertex at (1,2)

answer choices
1. y=(x-1)^2 - 2
2 . y=(x-1)^ 2 + 2
3 . y=(x+1)^2 - 2
4 . y=(x+1)^2 + 2​

Answer 1

The choice is correct.

`y = {(x -1)}^(2) + 2`

Step-by-step explanation

The equation of a parabola in vertex form is given by:

`y = a {(x -h)}^(2) + k`

where (h,k) is vertex of the parabola and 'a' is the leading coefficient of the parabola.

From the given options, the leading coefficient must be a=1.

We also have the vertex of the parabola at (1,2). This implies that h=1 and k=2.

We substitute these values into the formula to get,

`y = {(x -1)}^(2) + 2`

The second option is correct.