The equation y = x² - 2x + 5 expressed in vertex form is y = (x - 1)² + 4
How to determine the equation in vertex form
From the question, we have the following parameters that can be used in our computation:
y = x² - 2x + 5
Start by calculating the x-coordinate of the vertex of the equation using
h = -b/2a
Where
a = 1, b = -2 and c = 5
So, we have
h = 2/(2 * 1)
h = 1
The y-coordinate of the vertex of the equation is then calculated using
k = y(h) = h² - 2h + 5
So, we have
k = 1² - 2(1) + 5
k = 4
The equation in vertex form is represented as
y = a(x - h)² + k
Substitute the known values into the equation
y = (x - 1)² + 4
Hence, the equation is y = (x - 1)² + 4