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Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

 Apr 26, 2024
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                                       y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25    

 

group like terms              y  =  (–2x2 – 3x2) + (8x – 14x) + (–15 + 25)    

 

combine like terms           y  =  –5x2 – 6x + 10    

 

first derivitive                    dy/dx  =  –10x – 6    

 

set equal to zero                    0  =  –10x – 6    

                                           10x  =  –6   

                                               x  =  – 0.6    this is the x-coordinate of the vertex

 

sub x into original                   y  =  [ –5 • (–0.6)2 ]  –  [6 • (–0.6) ]  +  10    

                                               y  =  (–5 • 0.36)  –  (–3.6)  +  10    

                                               y  =  –1.8 + 3.6 + 10    

                                               y  =  11.8      this is the y-coordinate of the vertex

 

the vertex is at                        (–0.6 , 11.8)    

.

 Apr 26, 2024

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