MPM2D Solving Problems Involving Vertex Form Date: ______
When solving word problems, it is always important to draw a picture and label all relevant information. It is also important to include the axis. Read the problem carefully and consider all information given.
Ex 1: Determine the equation of the quadratic relation with vertex (1,1) and contains the point (5,-31).
Ex 2: A bridge is supported by a parabolic arch. Each end of the arch is set in concrete foundations that are on opposite sides of a river 374m wide. The top of the arch has a maximum height of 86m above the water.
Can a boat 42m tall pass under the bridge 50m from the shore?
Class/Homework:
1) Determine the equation of a quadratic relation given the vertex at (-3,2) and passing through the point (-1, 14).
2) The underside of a bridge forms a parabolic arch. The arch has a maximum height of 30 m and a width of 50 m. Can a sailboat pass under the bridge, 8 m from the axis of symmetry, if the top of its mast is 27 m above the water?
3) A model rocket is launched from the ground. After 20 s, the rocket reaches a maximum height of 2000 m. It lands on the ground after 40 s.
a) How high was the rocket after 15 s?
b) When was the rocket at a height of 1000 m?
4) The Lion’s Gate Bridge in Vancouver is a suspension bridge that spans a distance of 1516 m. Large cables are attached to the tops of the towers, 20 m above the road. The road is suspended from the large cables by many smaller vertical cables. The smallest vertical cable measures about 2m. Use this information to determine a quadratic model for the large cables.
5) A ball is thrown into the air from the roof of a building that is 25 m high. The ball reaches a maximum height of 45 m above the ground after 2 s. When will the ball hit the ground?
6) Eva can kick a football 34 m, reaching a maximum height of 16 m. To score a field goal, the ball must pass through the uprights which are 3.3 m above the ground. How far away from the uprights can Eva be and still score a field goal?