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Nonlinear functions SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

$y = x^{2} - 14 x + 22$

The given equation relates the variables $x$ and $y$ . For what value of $x$ does the value of $y$ reach its minimum?

Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.

ExplanationShow

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 $x = - \frac{b}{2 a}$ . 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 $x = - \frac{( - 14 )}{2 ( 1 )}$ , or $x = 7$ .

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