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Find the axis of symmetry and the vertex of the graph of: y=2x^(2)-4x+6

33. Find the axis of symmetry and the vertex of the graph of:\newliney=2x2−4x+6 y=2 x^{2}-4 x+6

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Q. 33. Find the axis of symmetry and the vertex of the graph of:\newliney=2x2−4x+6 y=2 x^{2}-4 x+6
  1. Rewrite in Vertex Form: Rewrite the equation in vertex form by completing the square.\newliney=2(x2−2x)+6y = 2(x^2 - 2x) + 6
  2. Complete the Square: Take half of the coefficient of xx, square it, and add it inside the parentheses. Remember to balance the equation by subtracting the same value outside the parentheses.\newliney=2(x2−2x+1)+6−2(1)y = 2(x^2 - 2x + 1) + 6 - 2(1)
  3. Simplify Equation: Simplify the equation. y=2(x−1)2+4y = 2(x - 1)^2 + 4
  4. Identify Vertex: Identify the vertex from the vertex form y=a(x−h)2+ky = a(x - h)^2 + k. Vertex (h,k)=(1,4)(h, k) = (1, 4)
  5. Find Axis of Symmetry: Find the axis of symmetry using the xx-value of the vertex.\newlineAxis of symmetry: x=1x = 1

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