The extreme value of the equation is at ( -5, - 4)
Completing the square method is one of the methods to find the roots of the given quadratic equation. In this method, we have to convert the given equation into a perfect square.
The extreme value is the maximum or minimum value of a quadratic function.
We have Y = 3x² + 30x + 71 using completing square method:
Y = 3 ( x² + 10x + 71 / 3 ) [ taking 3 common ]
Y = 3 ( ( x + 5 )² + 71 / 3 - 25 ) [ forming the perfect square ]
Y = 3 ( ( x + 5) ² - 4 / 3 )
now, converting the equation in the form of Y = 3(x+___)²+____
Y = 3 ( x + 5 )² - 4
then, comparing with the given equation we get values as (5, -4)
after putting x = -5 we get -4, so -4 is the minimum value (extreme) that Y = 3x² + 30x + 71 can achieve.
Hence, The extreme values of the equation is at (-5, -4)
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