Question

the x-coordinate (or t-coordinate) of the vertex is \boxed{} and represents how long the ball has been in the air when it hits the ground. the y-coordinate (or h-coordinate) of the vertex is \boxed{} and represents

Explanation:

Step1: Identify vertex coordinates

The vertex of the parabola is given as \((0.75, 9)\). So the \(x\)-coordinate (t - coordinate) of the vertex is the first value in the ordered pair, and the \(y\)-coordinate (h - coordinate) is the second value.

Step2: Determine t - coordinate

From the vertex \((0.75, 9)\), the \(t\)-coordinate (x - coordinate of vertex) is \(0.75\). This represents the time when the ball reaches its maximum height (since vertex of a parabola representing projectile motion is the maximum point).

Step3: Determine h - coordinate

From the vertex \((0.75, 9)\), the \(h\)-coordinate (y - coordinate of vertex) is \(9\). This represents the maximum height the ball reaches.

Answer:

The \(x\)-coordinate (or \(t\)-coordinate) of the vertex is \(\boldsymbol{0.75}\) and represents how long the ball has been in the air when it reaches maximum height.
The \(y\)-coordinate (or \(h\)-coordinate) of the vertex is \(\boldsymbol{9}\) and represents the maximum height the ball reaches.