Questions: Use the graph of the quadratic function f(x) = a(x-h)^2 + k to find the vertex, axis of symmetry, and the minimum or maximum value of the function.

Solution Steps

The vertex of the quadratic function \( f(x) = a(x-h)^2 + k \) is given by the coordinates \( (h, k) \). For the values provided, we have: \[ \text{Vertex} = (2, -3) \]

The axis of symmetry is the vertical line that passes through the vertex, which can be expressed as: \[ x = h \] Substituting the value of \( h \): \[ \text{Axis of Symmetry} = x = 2 \]

The function's minimum or maximum value occurs at the vertex's y-coordinate \( k \). Since the coefficient \( a = 1 \) is positive, the function has a minimum value. Thus: \[ \text{Minimum Value} = k = -3 \]

Final Answer