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The equation of a parabola is y=x2−10x+30y = x^2 - 10x + 30. 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+30y = x^2 - 10x + 30. 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+30y = x^2 - 10x + 30.
  3. Complete the square: Complete the square by adding and subtracting (10/2)2(10/2)^2, which is 2525, to the equation.\newliney=x2−10x+25+30−25y = x^2 - 10x + 25 + 30 - 25
  4. Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. \newliney=(x2−10x+25)+30−25y = (x^2 - 10x + 25) + 30 - 25
  5. Factor and simplify: Factor the perfect square trinomial and simplify the constants.\newliney=(x−5)2+5y = (x - 5)^2 + 5

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