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Find the maximum/minimum value of the quadratic function x2 – 10x = y + 40 by completing the square method.

 Jul 14, 2020
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Find the maximum/minimum value of the quadratic function x2 – 10x = y + 40 by completing the square method.

 

x2 - 10x = y + 40

 

Add 25 to both sides:   

x2 - 10x  + 25 = y + 65

 

Now the LHS can be written as:

(x - 5)2 = y + 65

 

Subtract 65 from both sides:

y = (x - 5)2 - 65

 

The minimum occurs when x = 5, at which point y = -65.

 Jul 14, 2020

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