Question

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

Answer 1

The answer you are looking for is the last choice (-2,-7).

if further proof and or work is needed this link will take you to a calculator that shows all work and the answer.

https://www.symbolab.com/solver/function-vertex-calculator/vertex%20f%5Cleft(x%5Cright)%3D3x%5E%7B2%7D%2B12x%2B5

:)

Answer 2

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.