Answer:
y = x² - 2x + 1
Step-by-step 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
From the graph (h, k) = (2, - 1), thus
y = a(x - 2)² - 1
To find a substitute a point on the curve (0, 1) into the equation
1 = 4a - 1 ( add 1 to both sides )
4a = 2 ( divide both sides by 4 )
a = =
, hence
y = (x - 2)² - 1 ← in vertex form
Expand the factor and simplify
y = (x² - 4x + 4) - 1
= x² - 2x + 2 - 1
= x² - 2x + 1 ← in standard form