SOLUTION: I'm having trouble completing the square and finding the vertex of the following function: {{{ y=-4x^2-12x+6 }}} Is making it into this the correct way to go about it?? {{

Algebra ->  Rational-functions -> SOLUTION: I'm having trouble completing the square and finding the vertex of the following function: {{{ y=-4x^2-12x+6 }}} Is making it into this the correct way to go about it?? {{      Log On


   

Question 215091: I'm having trouble completing the square and finding the vertex of the following function:
+y=-4x%5E2-12x%2B6+
Is making it into this the correct way to go about it??
+4%28x%5E2%2B3x-1.5%29+
Please help me!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-4x%5E2-12x%2B6 Start with the given expression.


-4%28x%5E2%2B3x-3%2F2%29 Factor out the x%5E2 coefficient -4. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient 3 to get 3%2F2. In other words, %281%2F2%29%283%29=3%2F2.


Now square 3%2F2 to get 9%2F4. In other words, %283%2F2%29%5E2=%283%2F2%29%283%2F2%29=9%2F4


-4%28x%5E2%2B3x%2Bhighlight%289%2F4-9%2F4%29-3%2F2%29 Now add and subtract 9%2F4 inside the parenthesis. Make sure to place this after the "x" term. Notice how 9%2F4-9%2F4=0. So the expression is not changed.


-4%28%28x%5E2%2B3x%2B9%2F4%29-9%2F4-3%2F2%29 Group the first three terms.


-4%28%28x%2B3%2F2%29%5E2-9%2F4-3%2F2%29 Factor x%5E2%2B3x%2B9%2F4 to get %28x%2B3%2F2%29%5E2.


-4%28%28x%2B3%2F2%29%5E2-15%2F4%29 Combine like terms.


-4%28x%2B3%2F2%29%5E2-4%28-15%2F4%29 Distribute.


-4%28x%2B3%2F2%29%5E2%2B15 Multiply.


So after completing the square, -4x%5E2-12x%2B6 transforms to -4%28x%2B3%2F2%29%5E2%2B15. So -4x%5E2-12x%2B6=-4%28x%2B3%2F2%29%5E2%2B15.


So y=-4x%5E2-12x%2B6 is equivalent to y=-4%28x%2B3%2F2%29%5E2%2B15.


So the equation y=-4%28x%2B3%2F2%29%5E2%2B15 is now in vertex form y=a%28x-h%29%5E2%2Bk where a=-4, h=-3%2F2, and k=15


Remember, the vertex of y=a%28x-h%29%5E2%2Bk is (h,k).


So the vertex of y=-4%28x%2B3%2F2%29%5E2%2B15 is because h=-3%2F2 and k=15.


You can graph this to confirm the answer.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
finding the vertex of the following function:
y=-4x^2-12x+6
--------------------------------
Rearrange:
-4x^2 - 12x = y -6
Factor out the -4
-4(x^2 + 3x + ?) = y-6 -4?
---
-4(x^2 + 3x + (3/2)^2) = y - 6 -4(9/4)
---
-4(x+(3/2))^2 = y -6 -9
---
-4(x+(3/2))^2 = y-15
---
Vertex at (-3/2 , 15)
---
graph%28400%2C300%2C-10%2C10%2C-10%2C20%2C-4x%5E2-12x%2B6%29
Cheers,
Stan H.