Question

What is the vertex of `y=x^2-2x+6`?

Answer 1

(1 , 5 )

Explanation:

The standard form of a quadratic function is :`y = ax^2+bx+c`

The function `y = x^2 - 2x + 6 " is in this form "`

with a = 1 , b = -2 and c = 6

The x-coordinate of the vertex is found using

`x = - b/(2a) = - (-2)/2 = 1`

substitute x = 1 into equation to obtain y-coordinate

hence: `y = (1)^2 - 2(1) + 6 = 5`

thus coordinates of vertex are ( 1 , 5 )

Here is the graph of the function.
graph{x^2-2x+6 [-20, 20, -10, 10]}