SOLUTION: Write the function f(x)=-5x^2-60x-181 in vertex form, and identify its vertex

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Question 1117682: Write the function f(x)=-5x^2-60x-181 in vertex form, and identify its vertex
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
-5%28x%5E2%2B12x%29-181
-5%28x%5E2%2B12x%2B36-36%29-181
-5%28%28x%2B6%29%5E2-36%29-181
-5%28x%2B6%29%5E2%2B5%2A36-181
-5%28x%2B6%29%5E2%2B180-181
-5%28x%2B6%29%5E2-1



---------------------------------------------mistake with sign------------------
5%28x%5E2-12x%29-181
5%28x%5E2-12x%2B36-36%29-181
5%28%28x-6%29%5E2-36%29-181
5%28x-6%29%5E2-5%2A36-181
5%28x-6%29%5E2-361
Vertex is (6, -361).

Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
Write the function f(x)=-5x^2-60x-181 in vertex form, and identify its vertex
~~~~~~~~~~~~~~~~~~~ 

  -5x^2 - 60x - 181 =    (complete the square. Notice that the leading coefficient is "minus 5").

= -5(x^2 + 12x) - 181 =

= -5(x^2 + 12x + 36 - 36) - 181 =

= -5(x^2 + 12x +36) + 180 - 181 = 

= -5(x+6)^2 - 1.


It is the vertex form.


The vertex is located at x= -6.  The function is a downward parabola.


It has the maximum at x= -6.  The value of this maximum is -1.


The vertex point is  (-6,-1).





Plot y = -5x%5E2+-+60x+-+181

Be aware:   The solution by  @josgarithmetic  (giving the answer (6,-361) for the vertex)  is   F A T A L L Y   W R O N G.

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    - HOW TO complete the square - Learning by examples
in this site.