Answer:
B
Step-by-step explanation:
We are given the quadratic function:
[tex]y=-2x^2+4x-6[/tex]
And we want to find its axis of symmetry.
First, the axis of symmetry is always a vertical line. Hence, it should be represented by x. Thus, we can eliminate choices A and D.
Next, the axis of symmetry for a quadratic is always the x-coordinate of its vertex point. The vertex for a quadratic equation is given by:
[tex]\displaystyle AOS=x=-\frac{b}{2a}[/tex]
For our function, a = -2, b = 4, and c= -6.
Therefore, our AOS is:
[tex]\displaystyle AOS=-\frac{4}{2(-2)}=-\frac{4}{-4}=1[/tex]
Hence, the equation of our axis of symmetry is x = 1.
B is our answer.
