The graph of g(x)=-(1)/(2)(x+3)^(2)-4 is translated 4 units right. What is the value of h when the equation of the transformed graph is written in vertex form? (A) -7 (B) 1 (C) -3 (D) 4 (E) -1 (F) 7

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Understand Translation Effect: Understand the effect of translating a graph to the right on the equation. Translating a graph horizontally to the right by 'k' units will result in a change in the x-component of the vertex form of the equation. The general form of the translation is: If g(x) = a(x - h)^2 + k, then the translated function g'(x) = a(x - (h + k))^2 + k. In this case, we are translating the graph 4 units to the right, so we will subtract 4 from the x-component of the vertex form.Apply Translation to Function: Apply the translation to the given function. The given function is g(x) = -(1/2)(x + 3)^2 - 4. To translate this function 4 units to the right, we replace x with (x - 4) in the equation. The new function will be h(x) = -(1/2)((x - 4) + 3)^2 - 4.Simplify Translated Equation: Simplify the equation of the translated function. Now we simplify the equation inside the parentheses: h(x) = -(1/2)(x - 4 + 3)^2 - 4 h(x) = -(1/2)(x - 1)^2 - 4 This is the vertex form of the translated function, where the vertex is at (h, k).Identify Vertex Value: Identify the value of h in the vertex form. From the vertex form h(x) = -(1/2)(x - 1)^2 - 4, we can see that the vertex is at (h, k) = (1, -4). Therefore, the value of h is 1.

The graph of $g(x)=-\frac{1}{2}(x+3)^{2}-4$ is translated $4$ units right. What is the value of $h$ when the equation of the transformed graph is written in vertex form? $\newline$ (A) $-7$ $\newline$ (B) $1$ $\newline$ (C) $-3$ $\newline$ (D) $4$ $\newline$ (E) $-1$ $\newline$ (F) $7$

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