Which equation is y = 2x2 - 8x + 9 rewritten in vertex form?

A. y = 2 (x - 2) 2 + 9

B. y = 2 (x - 2) 2 + 5

C. y = 2 (x - 2) 2 + 1

D. y = 2 (x - 2) 2 + 17

C

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

To obtain this form use the method of completing the square

Given

y = 2x² - 8x + 9

The coefficient of the x² term must be 1, so factor out 2 from 2x² - 8x

y = 2 (x² - 4x) + 9

To complete the square

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

y = 2 (x² + ( - 2) x + 4 - 4) + 9

= 2 (x - 2) ² - 8 + 9

= 2 (x - 2) ² + 1 → C