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?? {{

Question 215091: I'm having trouble completing the square and finding the vertex of the following function:

Is making it into this the correct way to go about it??

Please help me!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression.

Factor out the coefficient . This step is very important: the coefficient must be equal to 1.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

Distribute.

Multiply.

So after completing the square, transforms to . So .

So is equivalent to .

So the equation is now in vertex form where , , and

Remember, the vertex of is (h,k).

So the vertex of is because and .

You can graph this to confirm the answer.
Answer by stanbon(75887) (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)
---

Cheers,
Stan H.

RELATED QUESTIONS
I am having trouble finding the vertex of parabolas. I need to find the axes, roots, and... (answered by stanbon,josmiceli)
Find the vertex of the quadratic function y = x^2 - 8x - 5 by completing a square. Show... (answered by Fombitz)
Hi there, Im having trouble with this question: f(x)= X^2 - 4x +3 I need help... (answered by Fombitz)
I'm having problems with converting quadratics into vertex form, as well as solving... (answered by solver91311)
Hi I'm having trouble finding the vertex of this function. Can you help me? y = 6x^2 + (answered by solver91311)
I'm having trouble finding the correct answer. How do I solve this inequality?... (answered by MathLover1)
I am having trouble finding the Vertex of the quadratic equation of -0.2x^2 + 12x + 11... (answered by jrfrunner)
Graph the system below and write its solution. {4x+2y=6 {y=-2x+3 *It's either no... (answered by Fombitz)
Graph the system below and write its solution. {4x+2y=6 {y=-2x+3 *It's either no... (answered by Fombitz)