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

Question

campbell_st · Answer

well you need to distribute and collect like terms so the curve is in the form 

$$y = ax^2 + bx + c$$

then the line of symmetry is 

$$x = \frac{-b}{2 \times a}$$

hope it helps

anonymous · Answer

i know i need to simplify the equation, how do i do this?

campbell_st · Answer

well start with the perfect square 

$$(x -2)^2 =?$$

what does that become

anonymous · Answer

x squared minus 4?

campbell_st · Answer

nope 

$$(x -2)^2 = (x -2) \times (x  -2) $$

which can be written as 

$$x(x -2) - 2(x-2)$$

can you distribute this..?

anonymous · Answer

x^2-2x-2x+4?

campbell_st · Answer

great so its

$$x^2 - 4x + 4$$

so you now have 

$$y + 3x - 6 = -3(x^2 - 4x + 4) + 4$$

so distribute the -3

anonymous · Answer

-3x^2+12x-12+4

anonymous · Answer

then subtract the 3x from 12x?

campbell_st · Answer

that's good so its

$$y +3x - 6 = -3x^2 +12x -8$$

next add 6 to both sides of the equation

campbell_st · Answer

then lastly subtract 3 from both sides of the equation

campbell_st · Answer

oops 3x

campbell_st · Answer

so you will then have the coefficients for a and b

and can find the line of symmetry

campbell_st · Answer

an alternative method is to start by factoring the right side

$$y + 3(x -2) = -3(x -2)^2 + 4$$

subtract 3(x -2) from both sides

$$y = -3(x -2)^2 -3(x -2) + 4$$

so the coefficients are b = -3 and a = -3    and you are solving for (x -2)

so the line of symmetry

$$x -2 = \frac{-(-3)}{2 \times -3}$$

which is 

$$x - 2 = \frac{-1}{2}$$

now solve for x