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The image you provided shows a list of quadratic inequalities to be solved graphically. The heading says "Risolvere graficamente le seguenti disequazioni numeriche di secondo grado," which means "Solve graphically the following second-degree numerical inequalities." There are numbered problems (97 to 114) and their corresponding solutions or intervals of values where the inequality holds.

Here is a breakdown of some problems and their solutions:

### Example Problems:
- **97**: \( x^2 - 5x + 4 > 0 \)
  - Solution: \( x < 1 \) or \( x > 4 \)
  
- **99**: \( x^2 - 10x + 25 > 0 \)
  - Solution: \( x \neq 5 \) (the equation has a double root at 5, so inequality holds for all other values)
  
- **101**: \( x^2 - 64 \geq 0 \)
  - Solution: \( x \leq -8 \) or \( x \geq 8 \)
  
- **109**: \( \frac{1}{2}x^2 + 6x > 0 \)
  - Solution: \( 0 < x < 12 \)

- **111**: \( 3x^2 - 5 \geq 0 \)
  - Solution: \( x \leq -\frac{\sqrt{5}}{3} \) or \( x \geq \frac{\sqrt{5}}{3} \)

Would you like further details on any of these problems, or assistance solving any specific inequality?

### Relative Questions:
1. What is the graphical method for solving quadratic inequalities?
2. How do we determine the intervals where a quadratic inequality holds?
3. What are the common steps to solve \( ax^2 + bx + c \leq 0 \) inequalities algebraically?
4. How does the discriminant of a quadratic equation affect the solution of inequalities?
5. Can the solutions of quadratic inequalities be represented using set notation?

### Tip:
Always check the sign of the leading coefficient when solving quadratic inequalities; it affects the direction of the inequality.

Solve graphically the quadratic inequalities listed in the provided image.

This page explains how to solve various quadratic inequalities graphically and algebraically, including problems such as x² - 5x + 4 > 0 and 2x² - 7x - 15 ≥ 0. Learn about using the quadratic formula, the discriminant, and factorization to find intervals of solution.

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