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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=-3x^(2)-36 x-126 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=−3x2−36x−126 y=-3 x^{2}-36 x-126 \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=−3x2−36x−126 y=-3 x^{2}-36 x-126 \newlineAnswer:
  1. Calculate x-coordinate of vertex: To find the vertex of a parabola in the form y=ax2+bx+cy = ax^2 + bx + c, we can use the vertex formula x=−b2ax = -\frac{b}{2a} to find the x-coordinate of the vertex.\newlineHere, a=−3a = -3 and b=−36b = -36.\newlineLet's calculate the x-coordinate of the vertex.\newlinex=−(−36)/(2×−3)x = -(-36)/(2 \times -3)\newlinex=36/−6x = 36 / -6\newlinex=−6x = -6
  2. Substitute x-coordinate into equation: Now that we have the x-coordinate of the vertex, we can substitute it back into the original equation to find the y-coordinate of the vertex.\newliney=−3(−6)2−36(−6)−126y = -3(-6)^2 - 36(-6) - 126\newliney=−3(36)+216−126y = -3(36) + 216 - 126\newliney=−108+216−126y = -108 + 216 - 126\newliney=108−126y = 108 - 126\newliney=−18y = -18

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