What is the vertex form of y = 2x2 − 8x + 1?

y = 2(x - 2)² - 7

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

to obtain this form use the method of ' completing the square'

the coefficient of the x² term must be 1 → (factor out 2)

y = 2(x² - 4x + )

add/subtract ( coefficient of the x- term)² to x² - 4x

y = 2(x² + 2(- 2) + (- 2)² - (- 2)² + )

y = 2(x - 2)² + 2( - )= 2(x - 2)² - 7