Question

Marshall wants to determine the vertex of the quadratic function f(x)=x2-x+2. What is the function veryex?

Answer 1

vertex = (
`(1)/(2)`,
`(7)/(4)` )

Explanation:

Given a quadratic function in standard form f(x) = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

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

f(x) = x² - x + 2 ← is in standard form

with a = 1 and b = - 1, thus

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

Substitute x =
`(1)/(2)` into f(x) for corresponding y- coordinate

f(
`(1)/(2)` ) = (
`(1)/(2)` )² -
`(1)/(2)` + 2 =
`(1)/(4)` -
`(1)/(2)` + 2 =
`(7)/(4)`

vertex = (
`(1)/(2)`,
`(7)/(4)` )