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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. y=x^(2)-10 x+17 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=x2−10x+17 y=x^{2}-10 x+17 \newlineAnswer:

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Q. Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=x2−10x+17 y=x^{2}-10 x+17 \newlineAnswer:
  1. Identify Coefficient and Divide: The vertex form of a parabola is given by y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola. To find the vertex of the parabola y=x2−10x+17y = x^2 - 10x + 17, we need to complete the square to rewrite the equation in vertex form.
  2. Square the Coefficient: First, we take the coefficient of the xx term, which is −10-10, and divide it by 22 to get −5-5. Then we square −5-5 to get 2525.
  3. Complete the Square: Next, we add and subtract 2525 inside the parentheses to complete the square: y=(x2−10x+25)−25+17y = (x^2 - 10x + 25) - 25 + 17.
  4. Rewrite in Vertex Form: Now we can rewrite the equation as y=(x−5)2−8y = (x - 5)^2 - 8, which is now in vertex form.
  5. Find the Vertex: From the vertex form y=(x−5)2−8y = (x - 5)^2 - 8, we can see that the vertex (h,k)(h, k) of the parabola is (5,−8)(5, -8).

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