Atividade de Estudo 1 - Pré-Cálculo

Summary

Professor Ricardo welcomes students to the pre-calculus course, introducing their first activity inspired by Olympian Isa Leal's achievements. The activity revolves around a parabolic skateboarding ramp represented by the equation f(x) = ax² + c. Students are tasked with calculating the value of c, evaluating the function at specific points, and determining heights based on given distances. Ricardo emphasizes the importance of attending live classes, engaging with the material, and following instructions to achieve the best results, encouraging a collaborative and inquisitive learning environment.

Takeaways

• 😀 Welcome students to Pre-Calculus, taught by Professor Ricardo.
• 🏅 The first activity is inspired by skateboarder Isa Leal, who recently won an Olympic medal.
• 📊 The activity involves analyzing the equation of a skateboard ramp: f(x) = a * c * x^2.
• 📏 Important distances are given: OA = OD = 4 m and AB = DC = 3 m.
• 📍 Coordinates are specified for points O (0, 0), A (-4, 0), D (4, 0), and the height AD is 3 m.
• 🔍 The first task is to determine the value of c using the given distances.
• ➕ Item A requires calculating the expression f(2) + f(-2).
• 📐 Item B involves finding the height at x = 3 by calculating f(3).
• 📈 In Item C, students must find x such that f(x) = 9 for a height of 9 m.
• 🚶‍♂️ Item D asks for the value of f(12) for a distance of 12 m from point O.
• 📅 Participation in live sessions is essential for discussions and clarifying doubts.

Q & A

What is the main topic of the class led by Professor Ricardo?

The main topic of the class is precalculus, specifically focusing on a first activity inspired by the Paris Olympics.

What recent Olympic achievement is mentioned in the transcript?

The transcript mentions that Isa Leal, a skater, won her second Olympic medal, earning a bronze in Paris and a silver in Tokyo.

What is the mathematical function discussed in the activity?

The mathematical function discussed is f(x) = a * c * x^2, where 'c' is a real number.

What distances are given in the exercise related to the skate park?

The exercise states that the distances OA and OD are both equal to 4 meters, while distances AB and DC are both equal to 3 meters.

How are the coordinates of points A and D determined?

Point A has coordinates (-4, 0) and point D has coordinates (4, 0) since point O is at the origin (0, 0).

What does item A of the exercise ask the students to calculate?

Item A asks students to determine the value of the expression f(2) + f(-2) using the function provided.

What height must Raísa reach when positioned 3 m from the Y-axis?

Students need to calculate f(3) to determine Raísa's height when she is positioned 3 meters from the Y-axis.

What is the goal of item C in the activity?

Item C requires students to find the value of x for which f(x) = 9, indicating the height of 9 meters.

What distance does Raísa travel in item D?

In item D, Raísa travels a distance of 12 meters along the X-axis from point O.

What does Professor Ricardo emphasize about participation in live classes?

Professor Ricardo emphasizes the importance of student participation in live classes, encouraging them to ask questions and provide suggestions to maximize their learning.