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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)+8x+14 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+8x+14 y=x^{2}+8 x+14 \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+8x+14 y=x^{2}+8 x+14 \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=8b = 8.\newlineCalculate the x-coordinate of the vertex: x=−b2a=−82⋅1=−82=−4x = -\frac{b}{2a} = -\frac{8}{2\cdot 1} = -\frac{8}{2} = -4.
  2. Substitute xx into equation: Now that we have the xx-coordinate of the vertex, we can find the yy-coordinate by substituting x=−4x = -4 into the original equation.\newlineSubstitute x=−4x = -4 into y=x2+8x+14y = x^2 + 8x + 14 to find the yy-coordinate: y=(−4)2+8∗(−4)+14=16−32+14=−2y = (-4)^2 + 8*(-4) + 14 = 16 - 32 + 14 = -2.
  3. Find vertex coordinates: We have found the x-coordinate to be −4-4 and the y-coordinate to be −2-2. Therefore, the coordinates of the vertex of the parabola are (−4,−2)(-4, -2).\newlineCheck the calculations to ensure there are no math errors.

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