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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)-18 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=−2x2−18 y=-2 x^{2}-18 \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=−2x2−18 y=-2 x^{2}-18 \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 x=−b2ax = -\frac{b}{2a} to find the x-coordinate of the vertex.\newlineIn this equation, a=−2a = -2 and b=0b = 0 (since there is no xx term).\newlineLet's calculate the x-coordinate of the vertex.\newlinex=−b2a=−02×−2=0x = -\frac{b}{2a} = -\frac{0}{2 \times -2} = 0
  2. Find y-coordinate: Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting xx back into the original equation.y=−2x2−18y = -2x^2 - 18Substitute x=0x = 0:y=−2(0)2−18=−18y = -2(0)^2 - 18 = -18
  3. Determine vertex coordinates: The coordinates of the vertex are therefore (x,y)=(0,−18)(x, y) = (0, -18).

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