Characteristics of Parabolas Worksheet
Explore the key characteristics of parabolas, including vertex, axis of symmetry, focus, directrix, and direction of opening, through various exercises.
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Characteristics of Parabolas
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Read each question carefully and answer to the best of your ability. Show all your work where applicable.
1. The graph of a quadratic function is called a .
2. The highest or lowest point on a parabola is called the .
3. The is a line that divides the parabola into two symmetrical halves.
4. If the leading coefficient 'a' in y = ax² + bx + c is positive, the parabola opens .
5. Consider the parabola represented by the equation y = x² - 4x + 3. What are the coordinates of its vertex?
6. For the parabola y = -2x² + 8x - 5, state the equation of the axis of symmetry.
7. Which of the following equations represents a parabola that opens downwards?
y = 3x² + 2x - 1
y = -x² + 5x + 4
y = (x - 2)²
y = 0.5x² - 3
8. The vertex form of a quadratic equation is y = a(x - h)² + k. What do (h, k) represent?
The x-intercepts
The y-intercept
The vertex of the parabola
The focus of the parabola
9. A parabola can have two different y-intercepts.
True
False
10. The directrix of a parabola is a point.
True
False
11. Identify the vertex, axis of symmetry, and direction of opening for the parabola shown below.
Vertex:
Axis of Symmetry:
Direction of Opening: