Questions: g(x) = (x - 2)^2 + 3

Transcript text: g(x)=(x-2)^{2}+3

Solution

Step 1: Identify the function and its components

The given function is \( g(x) = (x - 2)^2 + 3 \). This is a quadratic function in vertex form, where \( a = 1 \), \( h = 2 \), and \( k = 3 \).

Step 2: Determine the vertex

The vertex of the function \( g(x) = (x - 2)^2 + 3 \) is at the point \( (h, k) \). Therefore, the vertex is \( (2, 3) \).

Step 3: Determine the direction of the parabola

Since the coefficient of the squared term \( (x - 2)^2 \) is positive (1), the parabola opens upwards.

The vertex of the function \( g(x) = (x - 2)^2 + 3 \) is at \( (2, 3) \), and the parabola opens upwards.

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