What is y=6x^2 +96x +388 in vertex form?
please show work

y = 6(x + 8)² + 4

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

Using the method of completing the square.

y = 6x² + 96x + 388

The coefficient of the x² term must be 1, so

factor out 6 from 6x² + 96x

y = 6(x² + 16x ) + 388

To complete the square

add/subtract (half the coefficient of the x- term)² to x² + 16x

y = 6(x² + 2(8)x + 64 - 64) + 388

  = 6(x + 8)² - 384 + 388

y = 6(x + 8)² + 4 ← in vertex form

a. the residual plot for model 1 has a random pattern and is a good fit for the data.

1

step-by-step explanation:

it's the only multiple of both and the least