A child throws a ball upward from the roof of a house. The trajectory is parabolic, according to the laws of physics. The height of the ball above the ground, h(x) (in meters) is given by the quadratic function: h(x) = -3x² + 6x + 4 where x is the horizontal distance from the house in meters. The goal of this tutorial is to graph this function and analyze and interpret the graph within the problem context. Show the following steps on the blackboard or paper as your instructor directs: d) What is the significance of the vertex in this problem context? e) Using all of the information from parts a) through d), sketch the quadratic function on its mathematical domain. Scale your graph appropriately and label all the important parts of the trajectory. f) Identify the practical domain on your graph and state the practical domain in interval notation. g) Use the quadratic formula to find the x-intercepts. Simplify fully and express exact answers. Plot these points on your graph. What is the meaning of these intercepts in the problem context?

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