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