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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x,y) point. y=x^(2)+2x+3 Answer:

Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x,y) (x, y) point.\newliney=x2+2x+3 y=x^{2}+2 x+3 \newlineAnswer:

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Q. Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x,y) (x, y) point.\newliney=x2+2x+3 y=x^{2}+2 x+3 \newlineAnswer:
  1. Calculate x-coordinate: To find the vertex of the parabola, we can use the vertex formula for a parabola in the form y=ax2+bx+cy = ax^2 + bx + c. The x-coordinate of the vertex is given by −b2a-\frac{b}{2a}. In our equation, a=1a = 1 and b=2b = 2.\newlineCalculate the x-coordinate of the vertex: x=−b2a=−22⋅1=−1x = -\frac{b}{2a} = -\frac{2}{2\cdot 1} = -1.
  2. Calculate y-coordinate: Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting x=−1x = -1 into the original equation.\newlineCalculate the y-coordinate of the vertex: y=(−1)2+2∗(−1)+3=1−2+3=2y = (-1)^2 + 2*(-1) + 3 = 1 - 2 + 3 = 2.
  3. Combine coordinates: Combine the xx and yy coordinates to form the vertex point.\newlineThe vertex of the parabola is at the point (−1,2)(-1, 2).

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