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

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

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Q. Complete the square to re-write the quadratic function in vertex form:\newliney=x2+2x−7 y=x^{2}+2 x-7 \newlineAnswer: y= y=
  1. Write Quadratic Equation: Write down the given quadratic equation.\newlineWe are given the quadratic function y=x2+2x−7y = x^2 + 2x - 7 and we need to convert it into vertex form.
  2. Identify Coefficient: Identify the coefficient of xx to complete the square.\newlineThe coefficient of xx is 22. To complete the square, we need to find (b/2)2(b/2)^2, where bb is the coefficient of xx.\newline$(\(2\)/\(2\))^\(2\) = \(1\)^\(2\) = \(1\)
  3. Add/Subtract to Complete Square: Add and subtract \((\frac{b}{2})^2\) inside the equation.\(\newline\)We add and subtract \(1\) inside the equation to complete the square.\(\newline\)\(y = x^2 + 2x + 1 - 1 - 7\)
  4. Group and Combine Terms: Group the perfect square trinomial and combine the constants. We group the terms to form a perfect square trinomial and combine the constants \(-1\) and \(-7\). \(y = (x^2 + 2x + 1) - 8\)
  5. Factor Perfect Square Trinomial: Factor the perfect square trinomial.\(\newline\)The perfect square trinomial \(x^2 + 2x + 1\) can be factored into \((x + 1)^2\).\(\newline\)\(y = (x + 1)^2 - 8\)
  6. Write in Vertex Form: Write the equation in vertex form.\(\newline\)The equation is now in vertex form, which is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex of the parabola.\(\newline\)\(y = (x + 1)^2 - 8\)

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