f(x) = (x - [tex]\frac{11}{2}[/tex])² - [tex]\frac{85}{4}[/tex]
the equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
given a quadratic in standard form : y = 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 - 11x + 9 is in standard form
with a = 1, b = - 11 and c = 9
[tex]x_{vertex}[/tex] = - [tex]\frac{-11}{2}[/tex] = [tex]\frac{11}{2}[/tex]
substitute this value into the equation for y- coordinate
y = ([tex]\frac{11}{2}[/tex])² - 11([tex]\frac{11}{2}[/tex]) + 9
= [tex]\frac{121}{4}[/tex] - [tex]\frac{242}{4}[/tex] + [tex]\frac{36}{4}[/tex] = - [tex]\frac{85}{4}[/tex]
f(x) = (x - [tex]\frac{11}{2}[/tex])² - [tex]\frac{85}{4}[/tex] ← in vertex form
