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Find the vertex of y = x^2 - 6x + 5

Worked through step by step. More quadratics.

Answer
(3,−4)\boxed{(3, -4)}

Substituting x=3x = 3 back into the original equation yields y=−4y = -4, confirming the vertex coordinates.

Problem: Find the vertex of the parabola y=x2−6x+5y = x^2 - 6x + 5.

Steps

  1. Identify coefficients
    a=1,b=−6,c=5a = 1, b = -6, c = 5
  2. Find the x-coordinate of the vertex using x=−b2ax = \frac{-b}{2a}
    x=−(−6)2(1)=62=3x = \frac{-(-6)}{2(1)} = \frac{6}{2} = 3
  3. Substitute the x-coordinate back into the equation to find the y-coordinate
    y=(3)2−6(3)+5y = (3)^2 - 6(3) + 5
  4. Evaluate the expression
    y=9−18+5=−4y = 9 - 18 + 5 = -4

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