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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=-2x^(2)-12 x-2 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=−2x2−12x−2 y=-2 x^{2}-12 x-2 \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=−2x2−12x−2 y=-2 x^{2}-12 x-2 \newlineAnswer:
  1. Calculate x-coordinate: To find the vertex of a parabola in the form y=ax2+bx+cy = ax^2 + bx + c, we can use the formula for the x-coordinate of the vertex, which is −b2a-\frac{b}{2a}. In this case, a=−2a = -2 and b=−12b = -12.\newlineCalculation: x=−(−12)/(2⋅−2)=12−4=−3x = -(-12)/(2 \cdot -2) = \frac{12}{-4} = -3
  2. Substitute xx into equation: Now that we have the xx-coordinate of the vertex, we can find the yy-coordinate by substituting x=−3x = -3 into the original equation.\newlineCalculation: y=−2(−3)2−12(−3)−2=−2(9)+36−2=−18+36−2=16y = -2(-3)^2 - 12(-3) - 2 = -2(9) + 36 - 2 = -18 + 36 - 2 = 16

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