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Which equation best matches the graph shown below? Answer y=(x-5)^(2)-2 y=-(x+5)^(2)-2 y=-(x-5)^(2)-2 y=(x+5)^(2)-2

Which equation best matches the graph shown below?\newlineAnswer\newliney=(x−5)2−2 y=(x-5)^{2}-2 \newliney=−(x+5)2−2 y=-(x+5)^{2}-2 \newliney=−(x−5)2−2 y=-(x-5)^{2}-2 \newliney=(x+5)2−2 y=(x+5)^{2}-2

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Full solution

Q. Which equation best matches the graph shown below?\newlineAnswer\newliney=(x−5)2−2 y=(x-5)^{2}-2 \newliney=−(x+5)2−2 y=-(x+5)^{2}-2 \newliney=−(x−5)2−2 y=-(x-5)^{2}-2 \newliney=(x+5)2−2 y=(x+5)^{2}-2
  1. Identify Vertex: Identify the vertex of the parabola from the graph. The vertex appears to be at (5,−2)(5, -2).
  2. Determine Direction: Determine the direction of the parabola. It opens downwards, indicating a negative coefficient for the quadratic term.
  3. Formulate Vertex Form: Formulate the vertex form of the equation using the vertex (5,−2)(5, -2) and the fact that the parabola opens downwards. The general vertex form is y=a(x−h)2+ky = a(x-h)^2 + k, where (h,k)(h, k) is the vertex. Here, h=5h = 5, k=−2k = -2, and aa is negative.
  4. Substitute Vertex: Substitute the vertex into the vertex form equation. Since the parabola opens downwards, aa is negative. The equation becomes y=−(x−5)2−2y = -(x-5)^2 - 2.

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