Question

Identify the vertex for the graph of y = 3x2 + 12x + 5.

(2, 41)
(2, 35)
(−2, −31)
(−2, −7)

Answer 1

Answer: The correct option is (D) (-2, -7).

Step-by-step explanation: We are given to identify the vertex for the graph of the following function :

`y=3x^2+12x+5~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

the vertex of the graph of the function
`y=a f(x-h)+k` is given by
`(h,k).`

From equation (i), we have

`y=3x^2+12x+5\\\\\Rightarrow y=3(x^2+4x)+5\\\\\Rightarrow y=3(x^2+4x+4)+5-12\\\\\Rightarrow y=3(x+2)^2-7\\\\\Rightarrow y=3\{x-(-2)\}^2+(-7).`

Therefore, the vertex of the graph of function (i) will be

`(h,k)=(-2,-7).`

Thus, (D) is the correct option.