Characteristics of Parabolas Worksheet
Explore the key characteristics of parabolas including vertex, axis of symmetry, focus, directrix, and direction of opening for Grade 11 Algebra students.
Includes
Standards
Characteristics of Parabolas
Name:
Date:
Score:
Read each question carefully and provide the best answer. Show all your work where applicable.
1. What is the vertex of the parabola given by the equation y = 2(x - 3)^2 + 1?
(3, 1)
(-3, 1)
(3, -1)
(-3, -1)
2. For a parabola that opens downwards, what can be said about the coefficient 'a' in the equation y = ax^2 + bx + c?
a > 0
a < 0
a = 0
a can be any real number
3. The is a line that divides the parabola into two symmetrical halves.
4. The point where the parabola changes direction is called the .
5. Consider the parabola given by the equation y = -x^2 + 4x - 3. Determine the coordinates of the vertex and the equation of the axis of symmetry.
6. The directrix of a parabola is a line perpendicular to the axis of symmetry.
True
False
7. Plot the vertex and draw the axis of symmetry for the parabola y = (x + 2)^2 - 4 on the graph below.
8. A parabolic arch has a height of 15 meters and a base width of 20 meters. If the vertex is at the highest point, write the equation of the parabola.
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