Question

the graph shows a parabola along with its vertex, focus, and directrix. determine the coordinates of the vertex and focus, and the equation of the directrix. the coordinates of the vertex are $(3,4)$. (simplify your answer. type an ordered pair.) the coordinates of the focus are $\square$. (simplify your answer. type an ordered pair.)

Explanation:

Step1: Locate the focus from the graph

By observing the graph, we can see that the focus is one unit to the right of the vertex \((3,4)\).

Step2: Calculate the coordinates of the focus

Since the \(x\) - coordinate of the vertex is \(3\) and we move \(1\) unit to the right (in the \(x\) - direction, \(y\) - coordinate remains the same as the vertex for this type of parabola opening horizontally), the \(x\) - coordinate of the focus is \(3 + 1=4\) and \(y\) - coordinate is \(4\).

Answer:

\((4,4)\)