Practice: Quadratic Equations Word Problems (with Vertex)

Last updated almost 3 years ago

5 questions

The first part of a rollercoaster ride is modelled after the equation:

Where y, is the height of the rollercoaster car from the ground and x, is the distance of the car from the start point.

At what distance from the starting point, will the distance from the ground be at a minimum.
Use completing the squares method to solve this.

Practice: Quadratic Equations Word Problems (with Vertex)

Last updated almost 3 years ago

5 questions

The first part of a rollercoaster ride is modelled after the equation:

Where y, is the height of the rollercoaster car from the ground and x, is the distance of the car from the start point.

At what distance from the starting point, will the distance from the ground be at a minimum.
Use completing the squares method to solve this.

The roller coaster car ascends after that reaches a maximum height it drops again, but this time the drop has the car plunging into the water. 
This drop is modelled as

At what x (distance from the start of the third phase of the ride) does the car plunge into the water, and at what point does it come out?

The cost, in dollars, to produce x units of a certain product is modelled by the equation 

How many units must be produced to minimise the cost, and what is the minimum cost?

Does the cost of production ever become zero, according to the vertex? Explain.

Try this yourself:
A wind turbine generates electricity by converting the kinetic energy of the wind into electrical energy. The power output, in kilowatts, of a wind turbine, is modelled by the equation


where
P is the power output in kilowatts and
v is the wind speed in meters per second. 

Practice: Quadratic Equations Word Problems (with Vertex)

At what distance from the starting point, will the distance from the ground be at a minimum.
Use completing the squares method to solve this.

Practice: Quadratic Equations Word Problems (with Vertex)

At what distance from the starting point, will the distance from the ground be at a minimum.
Use completing the squares method to solve this.

At what x (distance from the start of the third phase of the ride) does the car plunge into the water, and at what point does it come out?

How many units must be produced to minimise the cost, and what is the minimum cost?

Does the cost of production ever become zero, according to the vertex? Explain.

At what wind speed will the wind turbine generate its maximum power output, and what is that maximum power output?
Verify your answer using DESMOS

At what x (distance from the start of the third phase of the ride) does the car plunge into the water, and at what point does it come out?

How many units must be produced to minimise the cost, and what is the minimum cost?

Does the cost of production ever become zero, according to the vertex? Explain.

At what wind speed will the wind turbine generate its maximum power output, and what is that maximum power output?
Verify your answer using DESMOS

Practice: Quadratic Equations Word Problems (with Vertex)

At what distance from the starting point, will the distance from the ground be at a minimum. Use completing the squares method to solve this.

Practice: Quadratic Equations Word Problems (with Vertex)

At what distance from the starting point, will the distance from the ground be at a minimum. Use completing the squares method to solve this.

At what x (distance from the start of the third phase of the ride) does the car plunge into the water, and at what point does it come out?

How many units must be produced to minimise the cost, and what is the minimum cost?

Does the cost of production ever become zero, according to the vertex? Explain.

At what wind speed will the wind turbine generate its maximum power output, and what is that maximum power output?Verify your answer using DESMOS

At what x (distance from the start of the third phase of the ride) does the car plunge into the water, and at what point does it come out?

How many units must be produced to minimise the cost, and what is the minimum cost?

Does the cost of production ever become zero, according to the vertex? Explain.

At what wind speed will the wind turbine generate its maximum power output, and what is that maximum power output?Verify your answer using DESMOS

At what distance from the starting point, will the distance from the ground be at a minimum.
Use completing the squares method to solve this.

At what distance from the starting point, will the distance from the ground be at a minimum.
Use completing the squares method to solve this.

At what wind speed will the wind turbine generate its maximum power output, and what is that maximum power output?
Verify your answer using DESMOS

At what wind speed will the wind turbine generate its maximum power output, and what is that maximum power output?
Verify your answer using DESMOS