SOLUTION: hello! i need help getting the vertex form of y=-3x^2+12x-8. I have a test tommarow and i dont get it:(

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: hello! i need help getting the vertex form of y=-3x^2+12x-8. I have a test tommarow and i dont get it:(      Log On


   

Question 744398: hello! i need help getting the vertex form of y=-3x^2+12x-8. I have a test tommarow and i dont get it:(
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex form of the equation of a parabola is
y=a%28x-h%29%5E2%2Bk with a coefficient a and using the coordinates (h,k) of the vertex.

A SLOW AND EASY WAY:
If you expand the square in y=a%28x-h%29%5E2%2Bk you get
y=a%28x%5E2-2hx%2Bh%5E2%29%2Bk --> y=a%5Ex%5E2-2ahx%2Bah%5E2%2Bk
If you compare that to y=-3x%5E2%2B12x-8 you realize that:
the coefficient of x%5E2 is a=-3, and
the coefficient of x is -2ah=12
That gives you the values of a and h:
a=-3 was clear, and substituting that value in -2ah=12 you get
-2%2A%28-3%29%2Ah=12 --> 6h=12 --> h=12%2F6 --> h=2
Plugging those values into
y=a%28x-h%29%5E2%2Bk you get
y=-3%28x-2%29%5E2%2Bk --> y=-3%28x-2%29%5E2%2Bk --> y=-3%28x%5E2-4x%2B4%29%2Bk --> y=-3x%5E2%2B12x-12%2Bk
Comparing that last equation to y=-3x%5E2%2B12x-8, you realize that the independent term (the part without any x ) is
-12%2Bk=-8 --> k=-8%2B12 --> k=4
Plugging the values found for a, h, and k into y=a%28x-h%29%5E2%2Bk you get
highlight%28y=-3%28x-2%29%5E2%2B4%29.

THE FAST AND STEEP WAY that makes you look so smart:
y=-3x%5E2%2B12x-8 --> y=-3%28x%5E2-4x%29-8 (taking out (-3) as common factor from -3x%5E2%2B12x
y=-3%28x%5E2-4x%29-8 --> y=-3%28x%5E2-4x%2B4%29%2B3%2A4-8 (adding 3%2A4 and -3%284%29 which cancel out)
y=-3%28x%5E2-4x%2B4%29%2B3%2A4-8 --> y=-3%28x%5E2-4x%2B4%29%2B12-8 --> y=-3%28x%5E2-4x%2B4%29%2B4 --> highlight%28y=-3%28x-2%29%5E2%2B4%29.

THE MEMORIZED FORMULA WAY:
y=ax%5E2%2Bbx%2Bc --> y=a%28x%2Bb%2F2a%29%5E2%2B%284ac-b%5E2%29%2F4a
For y=-3x%5E2%2B12x-8, a=-3, b=12 and c=-8 so
b%2F2a=12%2F%282%2A%28-3%29%29=12%2F%28-6%29=-2 and
so
the vertex form is highlight%28y=-3%28x-2%29%5E2%2B4%29.

NOTE:
If your teacher favors the fast and steep way, show your teacher that way (even if you figured it out a different way on a separate piece of paper).