Algebra

 

                                               y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25   

 

 

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

 

The easiest way – the easiest way I know, anyway – is     

to set the first derivitive equal to zero, and solve for x.   

 

                                                ^dy/_dx  = –10x – 6   

 

                                                      0  =  –10x – 6     

                                                   10x  =  –6   

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

                                                                          plug it back into the original equation     

 

                                                        y  =  –5(–0.6²) – 6(–0.6) + 10      

                                                        y  =  –1.8 + 3.6 + 10   

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

 

                                                        The vertex is located at (–0.6 , 11.8)    

 

                                                         Verified the answer with Desmos Graphing Calculator.    

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