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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. y=-2x^(2)-20 x-64 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=−2x2−20x−64 y=-2 x^{2}-20 x-64 \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=−2x2−20x−64 y=-2 x^{2}-20 x-64 \newlineAnswer:
  1. Calculate x-coordinate: To find the vertex of a parabola given by the equation 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=−2a = -2 and b=−20b = -20.\newlineLet's calculate the x-coordinate of the vertex.\newlinex=−(−20)/(2×−2)=20−4=−5x = -(-20)/(2 \times -2) = \frac{20}{-4} = -5
  2. Substitute x-coordinate: 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=−2(−5)2−20(−5)−64y = -2(-5)^2 - 20(-5) - 64\newlineLet's calculate the y-coordinate.\newliney=−2(25)+100−64=−50+100−64=50−64=−14y = -2(25) + 100 - 64 = -50 + 100 - 64 = 50 - 64 = -14
  3. Find vertex coordinates: We have found both coordinates of the vertex. The vertex of the parabola is at the point (−5,−14)(-5, -14).

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