Question

Need help please this question is very confusing i would love some help

Answer 1

D

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

here (h, k) = (- 3, - 6), thus

y = a(x + 3)² - 6

To find a substitute (0, 0) into the equation

0 = 9a - 6 ⇒ a =
`(6)/(9)` =
`(2)/(3)`

y =
`(2)/(3)`(x + 3)² - 6 ← in vertex form

Expand (x + 3)² and distribute by
`(2)/(3)`

y =
`(2)/(3)`(x² + 6x + 9) - 6

=
`(2)/(3)` x² + 4x + 6 - 6

=
`(2)/(3)` x² + 4x ← in standard form