SOLUTION: Determine the vertex of the function by completing the square. -18x^2 + -177x + -190 An explanation of how to go about completing the square would be very much appreciate

Question 215000: Determine the vertex of the function by completing the square.
-18x^2 + -177x + -190

An explanation of how to go about completing the square would be very much appreciated! Thanks!

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 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

since and
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