📚 Topic Summary
The standard form of a parabola's equation is $y = a(x-h)^2 + k$, where $(h, k)$ is the vertex of the parabola. The coefficient 'a' determines whether the parabola opens upwards (if $a > 0$) or downwards (if $a < 0$), and also affects its width. A larger absolute value of 'a' means a narrower parabola, while a smaller absolute value means a wider parabola. The axis of symmetry is a vertical line that passes through the vertex, given by the equation $x = h$.
By identifying $a$, $h$, and $k$ from the equation, we can easily determine the vertex, direction of opening, and axis of symmetry. This worksheet will help you practice identifying these key properties!
🧠 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Vertex |
A. The line that divides the parabola into two symmetrical halves. |
| 2. Axis of Symmetry |
B. The highest or lowest point on the parabola. |
| 3. Standard Form |
C. $y = a(x-h)^2 + k$ |
| 4. 'a' Value |
D. Determines the direction and width of the parabola. |
| 5. Parabola |
E. A U-shaped curve. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
The standard form equation of a parabola is $y = a(x-h)^2 + k$. The _________ of the parabola is given by $(h, k)$. If 'a' is positive, the parabola opens _________. The _________ is the vertical line $x = h$.
🤔 Part C: Critical Thinking
Explain how changing the value of 'a' in the standard form equation affects the graph of the parabola. Give examples to illustrate your explanation.