y = x 2 - 14 x + 22 The given equation relates the variables x and y . For

Question

y = x 2 - 14 x + 22 The given equation relates the variables x and y . For what value of x does the value of y reach its minimum?

Accepted Answer

The correct answer is 7 . When an equation is of the form y = a x 2 + b x + c , where a , b , and c are constants, the value of y reaches its minimum when x = - b 2 a . Since the given equation is of the form y = a x 2 + b x + c , it follows that a = 1 , b = - 14 , and c = 22 . Therefore, the value of y reaches its minimum when x = - - 14 2 1 , or x = 7 .

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