Answer:
vertex = ([tex]\frac{1}{2}[/tex], [tex]\frac{7}{4}[/tex] )
Step-by-step explanation:
Given a quadratic function in standard form f(x) = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² - x + 2 ← is in standard form
with a = 1 and b = - 1, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]
Substitute x = [tex]\frac{1}{2}[/tex] into f(x) for corresponding y- coordinate
f([tex]\frac{1}{2}[/tex] ) = ([tex]\frac{1}{2}[/tex] )² - [tex]\frac{1}{2}[/tex] + 2 = [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{2}[/tex] + 2 = [tex]\frac{7}{4}[/tex]
vertex = ( [tex]\frac{1}{2}[/tex], [tex]\frac{7}{4}[/tex] )
