Question

Marsha wants to determine the vertex of the quadratic function f(x)=x^2-x+2. What is the function's vertex?

Answer 1

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

Explanation:

given a quadratic in standard form : ax² + bx + c : a ≠ 0

the x- coordinate of the vertex can be found as

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

f(x) = x² - x + 2 is in standard form

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

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

substitute this value into the function for the y-coordinate

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

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