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The equation of a parabola is y=x2−10x+19y = x^2 - 10x + 19. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______

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Q. The equation of a parabola is y=x2−10x+19y = x^2 - 10x + 19. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______
  1. Identify vertex form: Identify the vertex form of a parabola, which is y=a(x−h)2+ky = a(x - h)^2 + k.
  2. Start with given equation: Start with the given equation y=x2−10x+19y = x^2 - 10x + 19.
  3. Complete the square: To complete the square, take half of the coefficient of xx, which is −10/2=−5-10/2 = -5, and square it to get 2525.
  4. Add and subtract: Add and subtract 2525 inside the equation to complete the square: y=x2−10x+25−25+19y = x^2 - 10x + 25 - 25 + 19.
  5. Rewrite equation: Rewrite the equation grouping the perfect square trinomial: y=(x2−10x+25)−6y = (x^2 - 10x + 25) - 6.
  6. Factor perfect square trinomial: Factor the perfect square trinomial: y=(x−5)2−6y = (x - 5)^2 - 6.
  7. Equation in vertex form: The equation in vertex form is y=(x−5)2−6y = (x - 5)^2 - 6.

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