Question bank: Second Degree Function: Introduction

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Question 1:

Medium

What is the definition of a second degree function and what is its general form?

Second Degree Function: Introduction

Question 2:

Very Hard

A stone is thrown into the air from the ground with an initial velocity of 40 m/s, forming an angle of 45 degrees with the horizontal. Disregarding air resistance and considering the acceleration due to gravity as 10 m/s², the motion of the stone can be modeled by a function that describes the height h (in meters) of the stone relative to the ground as a function of time t (in seconds), given by h(t) = 40t * sin(45 degrees) - (1/2) * 10 * t^2. Considering that the value of sin(45 degrees) = 0.7071, answer: (1) What is the maximum height reached by the stone? (2) At what moment does the stone reach this height? (3) What is the total flight time of the stone, that is, the time interval between the launch and the moment the stone touches the ground again? Explain the behavior of the second-degree function in relation to these physical events, considering the context of the stone's launch.

Second Degree Function: Introduction

Theorical Question

Contextualized Question

Question 3:

Medium

A ball is kicked upwards from the ground with a force that makes it describe a trajectory that can be modeled by a quadratic function. This function represents the height h(t) of the ball in meters, t seconds after the kick, and is given by h(t) = -5t² + 20t. Considering the physical context of the situation, where h(t) is the height of the ball and t is the time elapsed since the kick, answer: 1) What is the maximum height the ball reaches and when does this occur? 2) What is the initial velocity of the ball at the moment of the kick? Justify your answers using the concepts of the vertex of the parabola and the derivative of the function h(t).

Second Degree Function: Introduction

Theorical Question

Contextualized Question

Question 4:

Medium

Second Degree Function: Introduction

Question 5:

Medium

A rocket was launched into space and its height h in relation to time t is given by the quadratic function h(t) = -16t² + 64t + 80, where the height h is measured in feet and the time t in seconds. What is the maximum height the rocket reaches and when does this happen?

Second Degree Function: Introduction

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