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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)-2x+4 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=x2−2x+4 y=x^{2}-2 x+4 \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=x2−2x+4 y=x^{2}-2 x+4 \newlineAnswer:
  1. Identify general form: Identify the general form of the quadratic equation.\newlineThe given parabola is in the form y=ax2+bx+cy = ax^2 + bx + c, where a=1a = 1, b=−2b = -2, and c=4c = 4.
  2. Use vertex formula: Use the vertex formula for a parabola.\newlineThe vertex of a parabola y=ax2+bx+cy = ax^2 + bx + c is given by the point (h,k)(h, k), where h=−b2ah = -\frac{b}{2a} and kk is the yy-value when x=hx = h.
  3. Calculate x-coordinate: Calculate the x-coordinate of the vertex hh. For the given equation y=x2−2x+4y = x^2 - 2x + 4, a=1a = 1 and b=−2b = -2. h=−(−2)/(2⋅1)=2/2=1h = -(-2)/(2\cdot1) = 2/2 = 1
  4. Calculate y-coordinate: Calculate the y-coordinate of the vertex kk. Substitute x=hx = h into the original equation to find kk. k=(1)2−2∗(1)+4=1−2+4=3k = (1)^2 - 2*(1) + 4 = 1 - 2 + 4 = 3
  5. Combine coordinates: Combine the coordinates to form the vertex point.\newlineThe vertex of the parabola is at the point (h,k)=(1,3)(h, k) = (1, 3).

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