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The equation of a parabola is y=x2−10x+24y = x^2 - 10x + 24. 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=x2−10x+24y = x^2 - 10x + 24. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______
  1. Find Value to Add: Complete the square by finding the value to add and subtract. Use (b2)2(\frac{b}{2})^2 where bb is the coefficient of xx.(−102)2=(−5)2=25\left(\frac{-10}{2}\right)^2 = (-5)^2 = 25.
  2. Add and Subtract Inside Equation: Add and subtract 2525 inside the equation.\newliney=x2−10x+25+24−25y = x^2 - 10x + 25 + 24 - 25.
  3. Group Perfect Square Trinomial: Group the perfect square trinomial and the constants.\newliney=(x2−10x+25)+24−25y = (x^2 - 10x + 25) + 24 - 25.
  4. Factor and Simplify: Factor the perfect square trinomial and simplify the constants.\newliney=(x−5)2−1y = (x - 5)^2 - 1.

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