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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+7 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+7 y=-x^{2}+2 x+7 \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+7 y=-x^{2}+2 x+7 \newlineAnswer:
  1. Find Vertex Formula: The vertex of a parabola given by the equation y=ax2+bx+cy = ax^2 + bx + c can be found using the vertex formula x=−b2ax = -\frac{b}{2a}. In this case, a=−1a = -1, b=2b = 2, and c=7c = 7.
  2. Calculate x-coordinate: Calculate the x-coordinate of the vertex using the formula x=−b2ax = -\frac{b}{2a}. Here, b=2b = 2 and a=−1a = -1, so x=−22∗(−1)=−2−2=1x = -\frac{2}{2*(-1)} = -\frac{2}{-2} = 1.
  3. Substitute x-coordinate: To find the y-coordinate of the vertex, substitute the x-coordinate back into the original equation y=−x2+2x+7y = -x^2 + 2x + 7. So, when x=1x = 1, y=−(1)2+2(1)+7=−1+2+7y = -(1)^2 + 2(1) + 7 = -1 + 2 + 7.
  4. Calculate y-coordinate: Calculate the y-coordinate by simplifying the expression from the previous step: y=−1+2+7=1+7=8y = -1 + 2 + 7 = 1 + 7 = 8.
  5. Combine coordinates: Combine the xx and yy coordinates to form the vertex point of the parabola. The vertex is at the point (1,8)(1, 8).

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