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How do you find the vertex of y=x^2+10x-21?

 Jun 12, 2023
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How do you find the vertex of y=x^2+10x-21?  

 

The first derivitive is the slope

of the curve at any point.                         y' = 2x + 10  

 

When the slope is zero, it means  

the curve is neither increasing nor  

decreasing, so set the first derivitive  

equal to zero and solve for x                     2x + 10  =  0  

                                                                         2x  =  –10  

                                                                          x  =  –5    This is the x-coordinate.  

 

Substitute –5 back into the 

original equation                                      y  =  x2 + 10x – 21  

                                                                y  =  (–5)2 + (10)(–5) – 21  

                                                                y  =  25 – 50 – 21  

                                                                y  =  –46           This is the y-coordinate.  

 

So the vertex of the parabola is at           (–5 , –46)  

 

You can take the original equation y=x^2+10x-21  

to the Desmos Graphing Calculator and see it  

drawn.  That's how I checked my answer.   

.

 Jun 12, 2023

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