Answer:
x=2
Step-by-step explanation:
The axis of symmetry can be calculated using the following formula:
[tex]Xv= \frac{-b}{2a}[/tex]
In order to use this formula, we need to have the function written in it's polynomial formula:
[tex]f(x)=ax^{2} +bx+c[/tex]
In order to do so, we have to isolate Y from the excercise's formula.
[tex]y=-2(x-2)^2-5[/tex]
Then we resolve the square of the binomial knowing that (a+b)^2=a^2+2.a.b+b^2
[tex](x-2)^2= x^2+2.x.(-2)+(-2)^2[/tex]
[tex](x-2)^2= x^2-4x+4[/tex]
Now we have that:
[tex]y=-2.(x^2-4x+4)-5[/tex]
[tex]y=-2x^2+8x-8-5[/tex]
[tex]y=-2x^2+8x-13[/tex]
As we have now the polynomyal formula, we know that a=-2, b=8 and c=-13. We supplant on the formula and get:
[tex]Xv= \frac{-b}{2a}[/tex]
[tex]Xv= \frac{-8}{2.(-2)}[/tex]
[tex]Xv= \frac{-8}{-4)}[/tex]
[tex]Xv= 2[/tex]
