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

1. campbell_st

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

2. anonymous

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

3. campbell_st

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

4. anonymous

x squared minus 4?

5. campbell_st

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

6. anonymous

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

7. campbell_st

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

8. anonymous

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

9. anonymous

then subtract the 3x from 12x?

10. campbell_st

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

11. campbell_st

then lastly subtract 3 from both sides of the equation

12. campbell_st

oops 3x

13. campbell_st

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

14. campbell_st

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