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.

Grade 11 Math AlgebraCharacteristics of Parabolas

Use This Worksheet

Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / FalseCustom

Standards

CCSS.MATH.CONTENT.HSF.IF.C.7.ACCSS.MATH.CONTENT.HSF.BF.B.3

8 sections · Free to use · Printable

← More Math worksheets for Grade 11

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.