Question

3.

Which of the following describes the parabola with the equation y = −x^2 − 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 = 0 and the vertex is (0, 6).

C. The axis of symmetry is x = −1 and the vertex is (−1, −3).

D. The axis of symmetry is x = 1.5 and the vertex is (1.5, 12.75).

Answer 1

A. The axis of symmetry is x = −1.5 and the vertex is (−1.5, 8.25).

Explanation:

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 .

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a. The axis of symmetry is x = −1.5 and the vertex is (−1.5, 8.25).

Step-by-step explanation:

The axis of symmetry is x = − b/2a

= -(-3) / 2(-1)

= 3/(-2)

= -1.5

the vertex => x = -1.5

y= -(-1.5)²-3(-1.5)+6 =

-2.25 +4.5+6= 8.25