Answers Based on the Graph:

1. Identify the Features:

   • A. Vertex: The vertex is $(2, 14)$, which represents the highest point on the graph.
   • B. Y-intercept: The y-intercept is $(0, 2)$, where the curve crosses the y-axis.
   • C. X-intercept: The x-intercepts are $(0, 0)$ and $(4.16, 0)$, where the curve crosses the x-axis.
   • D. Maximum or Minimum: The graph has a maximum point at the vertex $(2, 14)$.

2. Word Problem Based on the Graph:

   A projectile is launched from a height of 2 meters. Its height above the ground (in meters) is modeled by the equation $h(t) = -at^2 + bt + c$, where $t$ represents the time (in seconds) since launch.
   The projectile reaches its maximum height of 14 meters at 2 seconds after launch.
   a. How long does the projectile stay in the air before hitting the ground?
   b. What is the initial height of the projectile at launch?

Related Questions:

1. How do you determine the equation of a parabola given the vertex and y-intercept?
2. What is the physical significance of the vertex in projectile motion problems?
3. How do you calculate the total time the projectile is in the air?
4. How can you find the quadratic equation if the x-intercepts and one point are known?
5. What is the role of the x-intercepts in real-life applications like this graph?

Tip: The vertex of a parabola is a key feature in quadratic functions and represents either the maximum or minimum value of the function. It helps in solving real-world problems involving optimization or motion.