๐ Topic Summary
Parabolas are U-shaped curves defined by quadratic equations. The standard form equation, $y = ax^2 + bx + c$, reveals key features. The vertex represents the minimum or maximum point. The axis of symmetry is a vertical line passing through the vertex, dividing the parabola into two symmetrical halves. X-intercepts are the points where the parabola crosses the x-axis (also called roots or zeros), found by setting y = 0 and solving for x. The y-intercept is the point where the parabola crosses the y-axis (found by setting x = 0). Understanding these features allows you to quickly graph and analyze parabolic functions. The factored form $y = a(x-r_1)(x-r_2)$ is helpful in identifying the roots $r_1$ and $r_2$.
๐ง Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| 1. Vertex |
A. The vertical line that divides the parabola into two symmetrical halves. |
| 2. Axis of Symmetry |
B. The point where the parabola intersects the y-axis. |
| 3. X-intercept |
C. The highest or lowest point on the parabola. |
| 4. Y-intercept |
D. The point(s) where the parabola intersects the x-axis. |
| 5. Parabola |
E. A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. |
Write your answers here (e.g., 1-C, 2-A, etc.):
๐ Part B: Fill in the Blanks
A parabola is a _____ shaped curve. The _____ form of a parabola is given by $y = ax^2 + bx + c$. The vertex of a parabola represents the _____ or _____ point. The axis of _____ always passes through the vertex. The x-intercepts are also called the _____ or _____.
๐ค Part C: Critical Thinking
Explain how changing the value of 'a' in the equation $y = ax^2 + bx + c$ affects the shape and direction of the parabola.