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Complete the square to re-write the quadratic function in vertex form: y=x^(2)-7x-2 Answer: y=

Complete the square to re-write the quadratic function in vertex form:\newliney=x2−7x−2 y=x^{2}-7 x-2 \newlineAnswer: y= y=

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Complete the square to re-write the quadratic function in vertex form:\newliney=x2−7x−2 y=x^{2}-7 x-2 \newlineAnswer: y= y=
  1. Find Perfect Square Value: To complete the square, we need to find a value that, when added and subtracted to the xx-terms, creates a perfect square trinomial.\newlineFirst, we take the coefficient of the xx-term, which is −7-7, divide it by 22, and square it. This gives us (−7/2)2=49/4(-7/2)^2 = 49/4.
  2. Add/Subtract to Complete Square: We add and subtract this value inside the equation to complete the square. We must also ensure that we maintain the equation's balance by subtracting the same value outside the square.\newliney=x2−7x+(494)−(494)−2y = x^2 - 7x + \left(\frac{49}{4}\right) - \left(\frac{49}{4}\right) - 2
  3. Group and Combine Constants: Now, we group the perfect square trinomial and combine the constants outside the brackets.\newliney=(x2−7x+494)−494−2y = (x^2 - 7x + \frac{49}{4}) - \frac{49}{4} - 2
  4. Factor Perfect Square Trinomial: We can now factor the perfect square trinomial inside the brackets.\newliney=(x−72)2−494−2y = (x - \frac{7}{2})^2 - \frac{49}{4} - 2
  5. Combine Constant Terms: Next, we convert the constant terms to have a common denominator and combine them.\newlineSince 2=842 = \frac{8}{4}, we have:\newliney=(x−72)2−494−84y = (x - \frac{7}{2})^2 - \frac{49}{4} - \frac{8}{4}
  6. Simplify the Equation: Combine the constant terms to simplify the equation.\newliney=(x−72)2−574y = (x - \frac{7}{2})^2 - \frac{57}{4}

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