📚 Topic Summary
Solving quadratic equations by graphing involves finding the x-intercepts (also known as roots or zeros) of the parabola that represents the quadratic equation. The x-intercepts are the points where the parabola crosses the x-axis, meaning the y-value is zero at these points. By graphing the equation, you visually identify these points, providing the solutions to the quadratic equation. This method is particularly useful for visualizing the nature of the solutions - real and distinct, real and equal, or complex.
Graphing also allows you to estimate solutions, especially when they aren't whole numbers. However, it might not always provide exact answers, especially if the roots are irrational numbers. In such cases, algebraic methods like factoring or the quadratic formula are more precise.
🧠 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Quadratic Equation |
A. The highest or lowest point on a parabola. |
| 2. Parabola |
B. Solutions to the quadratic equation; points where the graph crosses the x-axis. |
| 3. Vertex |
C. An equation of the form $ax^2 + bx + c = 0$, where a ≠ 0. |
| 4. Roots/Zeros |
D. The vertical line that passes through the vertex, dividing the parabola into two symmetrical halves. |
| 5. Axis of Symmetry |
E. A U-shaped curve that represents a quadratic equation. |
✍️ Part B: Fill in the Blanks
A quadratic equation can be represented graphically as a __________. The solutions to the equation are the __________ of the graph, which are the points where the graph intersects the __________. The __________ of the parabola is the point where the parabola changes direction, and the __________ divides the parabola into two symmetrical halves.
🤔 Part C: Critical Thinking
Explain in your own words why graphing a quadratic equation is a useful method for finding its solutions. What are some limitations of this method?