Answer:
y =
x² - 2x + 1
Explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (2, - 1 ) , then
y = a(x - 2)² - 1
to find a substitute any other point that lies on the graph into the equation.
using (0, 1 )
1 = a(0 - 2)² - 1 ( add 1 to both sides )
2 = a(- 2)² = 4a ( divide both sides by 4 )
= a , that is
a =

y =
(x - 2)² - 1 ← equation in vertex form
expand (x - 2)² using FOIL
y =
(x² - 4x + 4) - 1 ← distribute parenthesis
y =
x² - 2x + 2 - 1 ← collect like terms
y =
x² - 2x + 1 ← in standard form