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The equation of a parabola is y=x2−8x+19y = x^2 - 8x + 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=x2−8x+19y = x^2 - 8x + 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=x2−8x+19y = x^2 - 8x + 19.
  3. Complete the square: Complete the square by adding and subtracting (8/2)2(8/2)^2, which is 1616, to the equation.\newliney=x2−8x+16+19−16y = x^2 - 8x + 16 + 19 - 16
  4. Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants.\newliney=(x2−8x+16)+19−16y = (x^2 - 8x + 16) + 19 - 16\newliney=(x−4)2+3y = (x - 4)^2 + 3

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