https://r2.erweima.ai/mathbot/image/1726673642891tkbs6dj6.pdf

The document you've uploaded contains problems on quadratic functions and uniformly accelerated motion. Below is a breakdown of the tasks:

### 1. Quadratic Function
You are tasked with finding the quadratic function \( f(x) \) that satisfies certain conditions. Each part requires:
- The equation of the quadratic function.
- Graphing the function.
- Identifying intersections with the axes, the image, zeros, positivity and negativity sets, and intervals of growth and decay.

Specific cases:
- (a) Given \( C_0 = \{-2; 1\} \) and a point \( (-3; 4) \) on the graph of \( f \).
- (b) The image of \( f \) is \( (-\infty; 3] \), and its positivity set \( C_+ = (-2; 6) \).
- (c) The positivity set corresponds to the inequality \( 2x^2 - 3x + 4 > 3 \), and the image coincides with the domain of \( h(x) = \sqrt{2x + 6} \). You are also required to calculate the distance between the vertex and the roots.

### 2. Uniformly Accelerated Motion (MRUV)
You are analyzing the motion of a car and a truck:
- Both vehicles move with constant acceleration: 4.4 m/s² for the car and 3.7 m/s² for the truck.
- At 9:00 AM, the distance between them is 20.75 m.
- After 5 seconds, they meet, with the car having traveled 157 m.
  
Questions:
- (a) Calculate the velocity of both vehicles at 9:00 AM.
- (b) Determine how far the truck traveled until the meeting point.
- (c) Find the velocity of each vehicle at the moment they are side by side.
- (d) Plot the position and velocity of both vehicles over time.

Would you like help solving one or more of these problems, or perhaps a specific part?

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**Relative Questions:**
1. How do you determine the equation of a quadratic function given points and conditions?
2. How do you solve inequalities involving quadratic functions?
3. What methods can be used to find the roots of a quadratic function?
4. How do you calculate the velocity of a vehicle undergoing uniformly accelerated motion?
5. What is the relationship between acceleration, distance, and time in uniformly accelerated motion?

**Tip:** When working with quadratic functions, always identify the vertex and roots first. These provide key insights into graph behavior.

The document you've uploaded contains problems on quadratic functions and uniformly accelerated motion. Below is a breakdown of the tasks:

1. Quadratic Function
You are tasked with finding the quadratic function f(x) that satisfies certain conditions.

2. Uniformly Accelerated Motion (MRUV)
You are analyzing the motion of a car and a truck:
- Both vehicles move with constant acceleration.

Would you like help solving one or more of these problems, or perhaps a specific part?

Solve problems involving quadratic functions and uniformly accelerated motion. Topics include identifying roots, graphing functions, calculating velocities, and determining distances using kinematic equations. Ideal for high school students in grades 10-12.

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