📚 Topic Summary
Graphing quadratic functions involves plotting parabolas, which are U-shaped curves. The standard form of a quadratic function is $f(x) = ax^2 + bx + c$, where 'a', 'b', and 'c' are constants. The sign of 'a' determines whether the parabola opens upwards (a > 0) or downwards (a < 0). The vertex, axis of symmetry, and intercepts are key features to identify when graphing.
Worksheets help you practice identifying these key features and plotting the graph accurately. By completing different types of questions, you will become confident in manipulating quadratic equations and visualizing their corresponding graphs.
🧮 Part A: Vocabulary
Match each term with its correct definition:
- Term: Vertex
- Term: Axis of Symmetry
- Term: Parabola
- Term: Quadratic Function
- Term: Roots
Definitions:
- The line that divides the parabola into two equal halves.
- The U-shaped curve representing a quadratic function.
- The highest or lowest point on the parabola.
- A function of the form $f(x) = ax^2 + bx + c$, where a ≠ 0.
- The x-intercepts of the parabola (where y=0).
✍️ Part B: Fill in the Blanks
Complete the paragraph with the correct terms:
The graph of a quadratic function is a __________. The __________ is the highest or lowest point on the parabola. The __________ is a vertical line passing through the vertex, dividing the parabola into two symmetrical halves. If the coefficient 'a' in $f(x) = ax^2 + bx + c$ is positive, the parabola opens __________. If 'a' is negative, the parabola opens __________.
🤔 Part C: Critical Thinking
Explain in your own words how changing the value of 'a' in the quadratic equation $f(x) = ax^2 + bx + c$ affects the shape and direction of the parabola.