Question

What is the equation of the axis of symmetry for the function shown below?

Answer 1

Answer:

x=2

Step-by-step explanation:

The axis of symmetry can be calculated using the following formula:

$Xv= \frac{-b}{2a}$

In order to use this formula, we need to have the function written in it's polynomial formula:

$f(x)=ax^{2} +bx+c$

In order to do so, we have to isolate Y from the excercise's formula.

$y=-2(x-2)^2-5$

Then we resolve the square of the binomial knowing that (a+b)^2=a^2+2.a.b+b^2

$(x-2)^2= x^2+2.x.(-2)+(-2)^2$

$(x-2)^2= x^2-4x+4$

Now we have that:

$y=-2.(x^2-4x+4)-5$

$y=-2x^2+8x-8-5$

$y=-2x^2+8x-13$

As we have now the polynomyal formula, we know that a=-2, b=8 and c=-13. We supplant on the formula and get:

$Xv= \frac{-b}{2a}$

$Xv= \frac{-8}{2.(-2)}$

$Xv= \frac{-8}{-4)}$

$Xv= 2$