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The equation of a parabola is y=x2−8x+23y = x^2 - 8x + 23. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______

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Full solution

Q. The equation of a parabola is y=x2−8x+23y = x^2 - 8x + 23. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______
  1. Complete the square: Complete the square for the xx-terms.(x2−8x+(82)2)−(82)2+23(x^2 - 8x + (\frac{8}{2})^2) - (\frac{8}{2})^2 + 23
  2. Calculate value: Calculate (8/2)2(8/2)^2 which is 1616. \newline(x2−8x+16)−16+23(x^2 - 8x + 16) - 16 + 23
  3. Combine like terms: Combine like terms −16+23-16 + 23 to get +7+7.\newline(x2−8x+16)+7(x^2 - 8x + 16) + 7
  4. Write in vertex form: Write the equation in vertex form.\newliney=(x−4)2+7y = (x - 4)^2 + 7

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