Question

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

(one-half, seven-quarters)
(one-half, three-halves)
(1, 1)
(1, 3)

Answer 1

Answer: The correct answer is the first option

Hope this helped ;)

Answer 2

Hi there!

`\large\boxed{\text{ Vertex at ((1)/(2), (7)/(4))}}`
`\large\boxed{\text{ Vertex at }((1)/(2), (7)/(4))}}`

We can use "Completing the Square" to solve:

f(x) = x² - x + 2

Group the variables. The "x" term's coefficient will be divided by two and squared for the third part of the trinomial. Remember to subtract by the third term:

f(x) = x² - x + (1/2)² + 2 - (1/2)²

Group:

f(x) = (x - 1/2)² + 2 - 1/4

Rewrite:

f(x) = (x - 1/2)² - 7/4

Thus, the first answer is correct.