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The equation of a parabola is y=x2+8x+22y = x^2 + 8x + 22. 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+22y = x^2 + 8x + 22. 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 quadratic term and the linear term.\newlineDivide the coefficient of xx by 22 and square it: (82)2=42=16\left(\frac{8}{2}\right)^2 = 4^2 = 16.\newlineAdd and subtract this value inside the equation.\newliney=x2+8x+16+22−16y = x^2 + 8x + 16 + 22 - 16
  2. Rewrite the equation: Rewrite the equation grouping the perfect square trinomial and combining the constants.\newliney=(x2+8x+16)+(22−16)y = (x^2 + 8x + 16) + (22 - 16)\newliney=(x+4)2+6y = (x + 4)^2 + 6

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