Algebra

 

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

 

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

 

take 1st derivitive               y'  =  –10x – 6    

and set equal to zero                  –10x – 6  =  0    

                                                   –10x        =  6    

                                                               x  =  –6/10 or –0.6     this is the x-coordinate    

                                                                                                 of the vertex    

substitute value of x    

into original equation           y  =  –5(–3/5)² – 6(–3/5) + 10    

                                            y  =  –5(9/25)   + 18/5     + 10    

                                            y  =  –9/5          + 18/5     + 10    

                                            y  =  59/5 or 11.8     this is the y-coordinate of the vertex     

 

The equation produces a downward opening parabola with its vertex at (–0.6 , 11.8)        

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