Question

Please show the steps you use :)

What are the coordinates of the vertex for f(x) = 3x^2 + 6x + 3? (1 point)

Group of answer choices

(−1, 0)

(3, 6)

(0, −1)

(6, 3)

Answer 1

vertex = (- 1, 0 )

Explanation:

Given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

x = -
`(b)/(2a)`

f(x) = 3x² + 6x + 3 ← is in standard form

with a = 3, b = 6 , then

`x_(vertex)` = -
`(6)/(6)` = - 1

Substitute x = - 1 into f(x) for corresponding y- coordinate of vertex

f(- 1) = 3(- 1)² + 6(- 1) + 3 = 3(1) - 6 + 3 = 3 - 6 + 3 = 0

vertex = (- 1, 0 )