Write v = 2x2 + 12x + 1 in vertex form.

A. y = (x+3) 2 - 17

B. y = (x+4)

C. y=2 (x+3) 2 - 17

D. y = 2 (x + 2) 2 + 12

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

Given

y = 2x² + 12x + 1

To express in vertex form use the method of completing the square.

The coefficient of the x² term must be 1, thus factor out 2 from 2x² + 12x

y = 2 (x² + 6x) + 1

add / subtract (half the coefficient of the x - term) ² to x² + 6x

y = 2 (x² + 2 (3) x + 9 - 9) + 1

= 2 (x + 3) ² - 18 + 1

= 2 (x + 3) ² - 17 → C

answer : C 2 (x-3) ²-17

Step-by-step explanation:

hello:

answer : C 2 (x-3) ²-17

calculate : 2 (x-3) ²-17 = 2 (x²-6x+9) - 17 = 2x²-12x+18-17

2 (x-3) ²-17 = 2x²-12x+1 ... (right)