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 (1,2). (simplify your answer. type an ordered pair.) the coordinates of the focus are (simplify your answer. type an ordered pair.)

Explanation:

Step1: Locate the focus on the graph

By observing the graph, we can see that the focus is 1 unit to the right of the vertex \((1,2)\).

Step2: Calculate the coordinates of the focus

Since the \(x\)-coordinate of the vertex is \(1\) and we move \(1\) unit to the right (in the \(x\)-direction), the \(x\)-coordinate of the focus is \(1 + 1=2\), and the \(y\)-coordinate remains the same as that of the vertex (\(y = 2\)). So the coordinates of the focus are \((2,2)\).

Answer:

\((2,2)\)