Answer:
A. The axis of symmetry is x = −1.5 and the vertex is (−1.5, 8.25).
Step-by-step 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
