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g(x)=−15(x+5)2−2g(x)=-\frac{1}{5}(x+5)^2-2

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Full solution

Q. g(x)=−15(x+5)2−2g(x)=-\frac{1}{5}(x+5)^2-2
  1. Identify Function Form: Identify the given function and its form.\newlineThe given function is g(x)=−15(x+5)2−2g(x) = -\frac{1}{5}(x+5)^2 - 2, which is already in vertex form.
  2. Determine Parabola Vertex: Determine the vertex of the parabola represented by the function.\newlineThe vertex form of a parabola is g(x)=a(x−h)2+kg(x) = a(x-h)^2 + k, where (h,k)(h, k) is the vertex of the parabola. In the given function, h=−5h = -5 and k=−2k = -2, so the vertex is (−5,−2)(-5, -2).
  3. Write Vertex Form: Write the vertex form of the function.\newlineThe vertex form of the function g(x)g(x) is already given as g(x)=−15(x+5)2−2g(x) = -\frac{1}{5}(x+5)^2 - 2, with the vertex at (−5,−2)(-5, -2).

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