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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)-8x 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=−2x2−8x y=-2 x^{2}-8 x \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=−2x2−8x y=-2 x^{2}-8 x \newlineAnswer:
  1. Factor out coefficient of x2x^2: The vertex form of a parabola is y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola. To find the vertex of the parabola y=−2x2−8xy = -2x^2 - 8x, we need to complete the square to convert the equation into vertex form.
  2. Complete the square: First, factor out the coefficient of x2x^2 from the xx terms: y=−2(x2+4x)y = -2(x^2 + 4x). We will complete the square inside the parentheses.
  3. Simplify the equation: To complete the square, we take half of the coefficient of xx, which is 44, square it, and add it inside the parentheses. We must also subtract it outside the parentheses to keep the equation balanced. However, since we factored out a −2-2, we need to add (−2)(-2) times the square of half the coefficient of xx to balance the equation: y=−2(x2+4x+4−4)y = -2(x^2 + 4x + 4 - 4).
  4. Distribute −2-2: Simplify the equation by combining the constant terms inside the parentheses and multiplying the −2-2 through the equation: y=−2((x+2)2−4)y = -2((x + 2)^2 - 4).
  5. Find vertex form: Now distribute the −2-2 to find the vertex form of the equation: y=−2(x+2)2+8y = -2(x + 2)^2 + 8.
  6. Identify vertex: The vertex form of the equation is now y=−2(x+2)2+8y = -2(x + 2)^2 + 8, which means the vertex (h,k)(h, k) is (−2,8)(-2, 8).

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