Question 1117682
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Write the function f(x)=-5x^2-60x-181 in vertex form, and identify its vertex
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<pre>
  -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).


{{{graph( 330, 330, -11, 3, -10.5, 3.5,
          -5x^2 - 60x - 181)
)}}}


Plot y = {{{-5x^2 - 60x - 181}}}
</pre>

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


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On completing the square see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Learning-by-examples-on-HOW-TO-complete-the-square.lesson>HOW TO complete the square - Learning by examples</A> 

in this site.