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The equation of a parabola is y=x2−8x+24y = x^2 - 8x + 24. 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+24y = x^2 - 8x + 24. 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. Calculate and Adjust: Start with the given equation y=x2−8x+24y = x^2 - 8x + 24.\newlineTo complete the square, calculate (8/2)2=42=16(8/2)^2 = 4^2 = 16, then add and subtract 1616 inside the equation.
  3. Rewrite Equation: Rewrite the equation as y=x2−8x+16+24−16y = x^2 - 8x + 16 + 24 - 16.
  4. Group and Combine: Group the perfect square trinomial and combine the constants: y=(x2−8x+16)+(24−16)y = (x^2 - 8x + 16) + (24 - 16).
  5. Simplify Constants: Simplify the constants: y=(x2−8x+16)+8y = (x^2 - 8x + 16) + 8.
  6. Factor Trinomial: Factor the perfect square trinomial: y=(x−4)2+8y = (x - 4)^2 + 8.

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