Question

height (in feet) is a function of time (in seconds) : find the line of symmetry and explain what it means in this context. show your work here line of symmetry: $x = 1.5$ the ball reached its highest point after 1.5 seconds line of symmetry: $x = 30$ the balls highest point was 30 feet above the ground line of symmetry: $y = 5$ the ball reached its highest point after 1.5 seconds line of symmetry: $y = 30$ the balls highest point was 30 feet above the ground

Explanation:

Step1: Identify the line of symmetry for a parabola

For a parabola (the graph of a quadratic function), the line of symmetry is a vertical line. The general form of a vertical line is \(x = a\). Looking at the options, \(x = 1.5\) and \(x = 30\) are vertical lines (\(y=5\) and \(y = 30\) are horizontal lines).

Step2: Analyze the context of the graph

The graph has time (in seconds) on the \(x -\)axis and height (in feet) on the \(y -\)axis. The line of symmetry of a parabola (which models the ball's height - time relationship) passes through the vertex (the maximum point for a parabola opening downwards). The \(x -\)coordinate of the vertex gives the time at which the ball reaches its maximum height. From the graph, the vertex (highest point) occurs at \(x = 1.5\) (since the \(x -\)axis is labeled as time in seconds).

Answer:

Line of symmetry: \(x = 1.5\); The ball reached its highest point after \(1.5\) seconds.