Question

What are the coordinates of the maximum or minimum value for the graph of the function x² - 4x +7 = y?

(-2, 3)
(2, -3)
(-2, -3)
(2, 3)

Answer 1

The vertex is (2,3)

The minimum value is 3

Explanation:

The given function is
`y=x^2-4x+7`

We complete the square to obtain the vertex form of the function.

`y=x^2-4x+4-4+7`

`y=(x-2)^2+3`

The vertex is (2,3)

The coefficient of the quadratic term is >0 therefore the vertex is the minimum point.