Question

Choose the correct vertex of the function f(x) = x2 - X + 2.

Answer 1

The vertex of the function is
`((1)/(2), (7)/(4))`

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

`f(x) = ax^(2) + bx + c`

It's vertex is the point
`(x_(v), y_(v))`

In which

`x_(v) = -(b)/(2a)`

`y_(v) = -(\Delta)/(4a)`

Where

`\Delta = b^2-4ac`

If a<0, the vertex is a maximum point, that is, the maximum value happens at
`x_(v)`, and it's value is
`y_(v)`.

f(x) = x² - X + 2.

Quadratic equation with
`a = 1, b = -1, c = 2`

So

`\Delta = b^2-4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7`

`x_(v) = -((-1))/(2) = (1)/(2)`

`y_(v) = -(-7)/(4) = (7)/(4)`

The vertex of the function is
`((1)/(2), (7)/(4))`