Question

11. Write y = 2x² +12x+14 in vertex form.

Please show work if possible so I know how to do it

Answer 1

y = 2(x + 3)² - 4

Explanation:

y = 2x² + 1 2x + 14

Move the constant (14) to the left side

y - 14 = 2x² + 12x

Now factor out 'a' , the coefficient of x² term

y - 14= 2(x² + 6x)

Divide the coefficient of 'x' by 2 ⇒ 6/2 = 3

Find the square of '3' and add it to x² + 6x ⇒ x² + 6x + 9

Multiply the square of 3 and add it to y - 14; 9*2 = 18

y- 14 = 2(x² + 6x + 9)

y - 14 + 18 = 2(x² + 6x + 9)

y + 4 = 2(x² + 6x +9)

y + 4 = 2(x + 3)²

y = 2(x + 3)² - 4

Vertex ( -3 , -4)