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

Hi there!

$\large\boxed{\text{ Vertex at (\frac{1}{2}, \frac{7}{4})}}$$\large\boxed{\text{ Vertex at }(\frac{1}{2}, \frac{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.

Answer 2

Answer: The correct answer is the first option

Hope this helped ;)