📚 Topic Summary
A linear-quadratic system involves one linear equation and one quadratic equation. Solving such a system means finding the points where the line and the parabola intersect. These points represent the solutions to both equations simultaneously. We can solve these systems graphically by plotting both equations and identifying intersection points, or algebraically using substitution or elimination methods. Understanding these systems allows us to model and solve problems in physics, engineering, and economics where linear and quadratic relationships interact.
🧠 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Linear Equation |
A. An equation whose highest degree is 2. |
| 2. Quadratic Equation |
B. A U-shaped curve on a graph. |
| 3. Parabola |
C. A method to solve systems by solving one equation for a variable and substituting into the other. |
| 4. Substitution |
D. A straight line on a graph. |
| 5. System of Equations |
E. A set of two or more equations considered together. |
(Match: 1-D, 2-A, 3-B, 4-C, 5-E)
✍️ Part B: Fill in the Blanks
A __________-quadratic system includes a linear equation and a __________ equation. Solving this system means finding the __________ points. The graphical solution involves plotting both equations and identifying the __________. Algebraically, you can use __________ or elimination.
(Answers: linear, quadratic, intersection, intersections, substitution)
🤔 Part C: Critical Thinking
Explain, in your own words, how the number of solutions (0, 1, or 2) for a linear-quadratic system is related to the way a line and a parabola can intersect on a graph.