Questions: Si la siguiente gráfica representa a la parábola x=1/4(y-2)^2+3. ¿Cuál es la gráfica que representa a x=-1/4(y-2)^2+3?

Transcript text: Si la siguiente gráfica representa a la parabola $x=\frac{1}{4}(y-2)^{2}+3$. ¿cual es la grafica que representa a $x=-\frac{1}{4}(y-2)^{2}+3$ ? Opciones: a) b) c)

Solution

Solution Steps

Step 1: Identify the given equation and its graph

The given equation is $ x = \frac{1}{4}(y - 2)^2 + 3 $. This is a parabola that opens to the right because the coefficient of the squared term $(y - 2)^2$ is positive.

Step 2: Identify the transformation of the given equation

The transformed equation is $ x = -\frac{1}{4}(y - 2)^2 + 3 $. This transformation involves changing the sign of the coefficient of the squared term, which means the parabola will open to the left instead of the right.

Step 3: Match the transformed equation to the correct graph

We need to find the graph that represents the equation $ x = -\frac{1}{4}(y - 2)^2 + 3 $. This graph should be a parabola that opens to the left with its vertex at $(3, 2)$.

Final Answer

The correct graph is option (b).

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