3. Which of the following describes the parabola with the equation y = -x2 – 3x + 6?
A. The axis of symmetry is x = -1.5 and the vertex is (-1.5, 8.25).
B. The axis of symmetry is x = -1 and the vertex is (-1, -3).
C. The axis of symmetry is x = 0 and the vertex is (0, 6).
D. The axis of symmetry is x = 1.5 and the vertex is (1.5, 12.75).

Hello Papi :D

I will solve the problem by applying the perfect square trinomial. In this way we obtain the canonical form. Another way would be to derive the function, but I don't know if you're familiar with it.

First: let us take out the common factor: , since we remember that the canonical form is characterized as follows:

Then, it remains:

Then: the coefficient of the variable We divided it between , And we square it (they will be one positive and one negative). In our case:

Let's accommodate terms to make it easier:

Can be written as :

Now, what is underlined is our perfect square trinomial, let us recall its form:

Applying the same principle we are left:

Applying distributive property we get:

Therefore it will have its vertex in:

The axis of symmetry is a straight line that makes the function to be projected being , for this you need some reference point, for the parabola you need the coordinate in of the vertex.

For which the axis of symmetry is .

I love you so much !