Algebra

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

                                  y  =  –2x² + 8x – 15 – 3x² – 14x + 25    

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

set the first derivitive to zero    

                                   –10x – 6 = 0     ==>>     x = – 6 / 10  =  – 0.6    

plug this x back into the equation    

                                        y  =  –5•(–6/10)² – 6•(–6/10) + 10    

                                        y  =  –180 / 100  +  36 / 10  +  10    

                                        y  =  –180 / 100  +  360 / 100  +  1000 / 100    

                                        y  =  1180 / 100  =  59 / 5  =  11.8    

Thus, the vertex is at (–0.6, 11.8)    

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