📊 Quadratic Graph Plotter
📌 Understanding Quadratic Graphs
A quadratic equation in the form **y = ax² + bx + c** represents a parabolic curve, where:
- **a** determines the direction and steepness of the parabola.
- **b** affects the horizontal shift of the graph.
- **c** represents the y-intercept of the graph.
📌 Examples of Quadratic Equations
| Equation | a | b | c |
|---|---|---|---|
| y = x² – 4x + 3 | 1 | -4 | 3 |
| y = 2x² + 5x – 7 | 2 | 5 | -7 |
| y = -x² + 3x + 2 | -1 | 3 | 2 |
❓ FAQs
Q1: How do I plot a quadratic graph?
✅ A quadratic graph is plotted using the equation **y = ax² + bx + c**, where a, b, and c are coefficients that shape the parabola.
Q2: What does the coefficient a represent?
✅ The coefficient **a** determines if the parabola opens upward (positive a) or downward (negative a) and affects the width.
Q3: How does the value of c affect the graph?
✅ The coefficient **c** is the y-intercept, where the parabola crosses the y-axis.
Q4: What happens if a is zero?
✅ If **a = 0**, the equation reduces to a linear function, resulting in a straight-line graph.
Q5: Can a quadratic equation have no real roots?
✅ Yes, if the discriminant (**b² – 4ac**) is negative, the equation has no real roots, and the graph does not cross the x-axis.