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

ANSWER

The choice is correct.

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

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.