Complete the square to rewrite y = x2 + 6x + 3 in vertex form. then state whether the vertex is a maximum or a minimum and give its coordinates.

a. maximum at (3, –6)
b. minimum at (3, –6)
c. minimum at (–3, –6)
d. maximum at (–3, –6)

Step-by-step explanation:

The given expression is:

So, to complete the square, we first have to find the squared quotient between the second-term coefficient and 2, the add and subtract this number at the same time in the expression, like this:

Then,

Now, we just have to group the terms that can be factorized:

Then, the factorization would be made using the squared root of and , which is:

At the end, we just operate independent number outside the factorization:

So, according to the complete square of the expression, we can see that the vertex has coordinates , which is a minimum, because the squared coefficient is positive, that means the parabola is concave up.

The reason why the vertex has that coordinates is because the explicit expression of a parabola is:

Where is vertex coordinates.

Therefore, the answer is C.