๐ Topic Summary
Quadratic functions are powerful tools for modeling real-world situations involving parabolic paths or relationships that increase or decrease at an increasing rate. This activity focuses on applying quadratic functions to solve word problems, requiring you to translate the given scenario into a quadratic equation, solve for the unknown variable(s), and interpret the solution in the context of the problem. Common applications include projectile motion (e.g., the height of a ball thrown in the air), optimization problems (e.g., maximizing the area of a rectangular garden), and revenue/profit analysis.
๐ง Part A: Vocabulary
| Term |
Definition (Mixed Up) |
| Vertex |
The point where the parabola intersects the y-axis. |
| Axis of Symmetry |
The highest or lowest point on a parabola. |
| Y-intercept |
A line that divides the parabola into two symmetrical halves. |
| Root |
The solutions to the quadratic equation (where the parabola crosses the x-axis). |
| Parabola |
The U-shaped curve of a quadratic function. |
โ๏ธ Part B: Fill in the Blanks
A quadratic function is a polynomial function of degree _____. The graph of a quadratic function is a _____. The standard form of a quadratic equation is $f(x) = ax^2 + bx + c$, where a, b, and c are _____. To find the maximum or minimum value, we look at the _____ of the parabola. Word problems often require us to find the _____, y-intercept, or vertex to solve them.
๐ค Part C: Critical Thinking
Describe a real-world scenario (different from those mentioned above) where a quadratic function could be used to model and solve a problem. Explain what the variables would represent and what the vertex would signify in that context.