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-16 Answer:

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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-16 Answer:

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Identify Vertex Form: The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. To find the vertex of the given parabola, we need to complete the square to transform the equation into vertex form.Factor Out Coefficient: The given equation is y = -x^2 - 8x - 16. To complete the square, we need to factor out the coefficient of the x^2 term from the x terms.Find Completing Number: Factoring out -1 from the x terms, we get y = -(x^2 + 8x) - 16. Now we need to find the number that completes the square for the expression x^2 + 8x.Add/Subtract Completing Number: To complete the square, we take half of the coefficient of x, which is 8/2 = 4, and square it, which gives us 4^2 = 16. We add and subtract this number inside the parentheses to maintain equality.Simplify Expression: Adding and subtracting 16 inside the parentheses, we get y = -(x^2 + 8x + 16 - 16) - 16. This simplifies to y = -(x + 4)^2 + 16 - 16.Finalize Vertex Form: Simplifying the equation, we get y = -(x + 4)^2. Since there is no constant term outside the parentheses after completing the square, the vertex form of the equation is y = -(x + 4)^2 + 0.Determine Vertex Point: The vertex of the parabola is the point (h, k) from the vertex form y = a(x - h)^2 + k. In our equation, h = -4 and k = 0, so the vertex is (-4, 0).

Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an $(x, y)$ point. $\newline$ $y=-x^{2}-8 x-16$ $\newline$ Answer:

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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x,y) (x, y) (x,y) point.\newliney=−x2−8x−16 y=-x^{2}-8 x-16 y=−x2−8x−16\newlineAnswer:

Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an $(x, y)$ point. $\newline$ $y=-x^{2}-8 x-16$ $\newline$ Answer: