Answer:
vertex = ( [tex]\frac{1}{2}[/tex], [tex]\frac{7}{4}[/tex])
Step-by-step explanation:
given a quadratic in standard form : ax² + bx + c : a ≠ 0
the x- coordinate of the vertex can be found as
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² - x + 2 is in standard form
with a = 1, b = - 1 and c = 2
[tex]x_{vertex}[/tex] = - [tex]\frac{-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]
substitute this value into the function for the y-coordinate
y = ([tex]\frac{1}{2}[/tex])² - [tex]\frac{1}{2}[/tex] + 2 = [tex]\frac{7}{4}[/tex]
vertex = ( [tex]\frac{1}{2}[/tex], [tex]\frac{7}{4}[/tex])
