What is the vertex form of the quadratic y = 3x^2 + 18x - 4?

y = 3 (x + 3) ² - 31

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

take out a common factor of 3 from the first 2 terms

y = 3 (x² + 6x) - 4

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

y = 3 (x² + 2 (3) x + 9 - 9) - 4

y = 3 (x + 3) ² - 27 - 4

y = 3 (x + 3) ² - 31 ← in vertex form