What are the vertex, focus, and directrix of the parabola whose equation is \( y-4=\frac{1}{4}(x-7)^{2} \) ? vertex \( =(\square) \) focus \( =(\square \)

The given equation of the parabola is   y – 4 = (1/4)(x – 7)². This equation is in the vertex form of a parabola that opens upward or downward:   y – k = (1/(4p))·(x – h)², where (h, k) is the vertex and p is the distance from the vertex to the focus. From the equation:   1/(4p) = 1/4 ⟹ p = 1, and the vertex (h, k) is:   (7, 4). Since the parabola opens upward (because the coefficient 1/4 is positive), the focus lies p units above the vertex. Therefore:   Focus = (7, 4 + 1) = (7, 5). The directrix is the horizontal line p units below the vertex:   Directrix: y = 4 – 1 = 3. So, the answers are:  Vertex = (7, 4)  Focus = (7, 5)  Directrix = y = 3.