Question

What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)2 + 4?

Answer 1

 What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)2 + 4?


A. x=3/2

Answer 2

Answer:

Option: A is the correct answer.

              The axis of symmetry is:

                      A.    x=3/2      

Step-by-step explanation:

We are given a graph as:

$y+3x-6=-3(x-2)^2+4$

and

$y=-3(x-2)^2+4+6-3x$

and

$y=-3[(x-2)^2+x]+10\\\\i.e.\\\\y=-3[x^2+4-4x+x]+10\\\\i.e.\\\\y=-3[x^2-3x+4]+10$

This equation could also be written in the form:

$y=-3[x^2-3x+4-\dfrac{9}{4}+\dfrac{9}{4}]+10\\\\i.e.\\\\y=-3[(x-\dfrac{3}{2})^2+4-\dfrac{9}{4}]+10\\\\i.e.\\\\y=-3[(x-\dfrac{3}{2})^2+\dfrac{7}{4}]+10\\\\i.e.\\\\y=-3(x-\dfrac{3}{2})^2-3\times \dfrac{7}{4}+10\\\\i.e.\\\\y=-3(x-\dfrac{3}{2})^2+\dfrac{19}{4}$

Now, we know that for any general equation of the type:

$y=a(x-h)^2+k$

The axis of symmetry of the graph of the equation is:

$x=h$

Here we have:

$h=\dfrac{3}{2}$

            Hence, the answer is: Option: A