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Applications of Quadratic Equations

Applications of Quadratic Equations. Example 1: The path of a baseball is given by the equation below, where h is height and d is the horizontal distance in metres. . a) Sketch this motion . b) What is the maximum height of the ball? c) What is the horizontal distance when this occurs?

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Applications of Quadratic Equations

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  1. Applications of Quadratic Equations

  2. Example 1: The path of a baseball is given by the equation below, where h is height and d is the horizontal distance in metres. • a) Sketch this motion

  3. b) What is the maximum height of the ball? • c) What is the horizontal distance when this occurs? • d) What is the height of the ball when the horizontal distance is 50m? • e) Find another horizontal distance where the height is the same as in part d.

  4. 2. A cannonball is shot into the air. Its height can be described by the equation h = -3(t – 1)(t – 9) where h is height in feet and t is time in seconds. Sketch this relation.

  5. 2. A cannonball is shot into the air. Its height can be described by the equation h = -3(t – 1)(t – 9) where h is height in feet and t is time in seconds. • a) What are the zeroes of this relation? _________ and _________ b) What do the zeroes mean in this situation? c) Use the axis of symmetry to find the vertex and explain what the vertex means for the cannonball.

  6. 3. Find the equation of a parabola that has a vertex of (-2,3) and passes through the point (-4,-9).

  7. 4. A firework leaves at a height of 1 m above the ground and maximum height of 109 m at a horizontal distance of 3 m. • a) Determine an equation to model the height versus the horizontal distance. • b) Determine the height at a horizontal distance of 1 m.

  8. 5. The middle part of a bridge is in the shape of a concave up parabola. The lowest point of the bridge is 50m above the water and the two towers are 120m high and 500m apart. • a) Sketch the function with the vertex at the lowest point, and the zeroes at the tops of the towers.

  9. The middle part of a bridge is in the shape of a concave up parabola. The lowest point of the bridge is 50m above the water and the two towers are 120m high and 500m apart. b) Determine the equation of the height of this bridge above the lowest point in terms of its horizontal distance if the vertex is at the lowest point. Graph the parabola.

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