Grade 11 · Math · Algebra 2

11th grade Parabolas: focus, directrix and equations worksheet

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Parabolas: focus, directrix and equations

Grade 11 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Noah draws a lamp reflector's curve as (x − 2)² = 8(y + 1). The bulb goes at the focus. Where is the focus?
Ren draws the parabola (y − 3)² = 12(x − 1) on graph paper. Where is its focus?
Tala draws a fountain's arc of water as (x + 4)² = -12(y − 2). Where is its focus?
Zee sketches the parabola (y + 2)² = -16(x + 3) on graph paper. Where is its focus?
5.
Esme draws a lamp reflector's curve as (x − 1)² = 12(y − 2). Which line is the directrix?
- y = -1
- y = -5
- y = 5
- y = -10
6.
Jun draws the parabola (y + 3)² = 8(x − 2) on graph paper. Which line is its directrix?
- x = -6
- x = 0
- x = 4
- x = -4
7.
Luz draws a fountain's arc of water as (x + 2)² = -16(y − 1). Which line is its directrix?
- y = 5
- y = 17
- y = -3
- y = 3
8.
Milo sketches the parabola (y − 4)² = -20(x + 1) on graph paper. Which line is its directrix?
- x = 6
- x = 4
- x = -6
- x = 19
9.
Noah draws the parabola (y − 3)² = 8(x + 1) on graph paper. Which line is its axis of symmetry?
- x = 1
- y = -3
- y = 3
- x = -1
10.
Jun plans a fountain's arc of water with focus (0, -2) and directrix y = 2. Which equation is the arc?
- x² = -2y
- y² = -8x
- x² = -8y
- x² = -16y

11th grade Parabolas: focus, directrix and equations worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Parabolas: focus, directrix and equations. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the focus, directrix and axis of a parabola from its equation, using 4p.
I can write a parabola's equation from its focus and directrix: the vertex is halfway, and p is half the gap.
I can complete the square to turn x² − 8x − 8y + 8 = 0 into (x − 4)² = 8(y + 1).

Standard: G-GPE.A.2

Words to know

parabola: Every point as far from one marked point as from one line.

focus: The marked point inside the curve.

directrix: The marked line outside the curve.

vertex: The turning point, halfway between the focus and the directrix.

p: The distance from the vertex to the focus; the equation shows 4p.

axis of symmetry: The mirror line through the vertex and the focus.

Common mistakes

Your child used the whole number in the equation as the distance to the focus, instead of a quarter of it.

Your child put the focus distance where four times it belongs.

Your child put the directrix on the same side of the vertex as the focus.

What to say

Ask: if 4p = 12, what is p?

Ask: if p = 3, what number goes in the equation?

Ask: which side is the focus on, and where must the line go?

Questions parents ask

What is the most common mistake with parabolas: focus, directrix and equations?

Your child used the whole number in the equation as the distance to the focus, instead of a quarter of it.

How can I help my child with parabolas: focus, directrix and equations?

Ask: if 4p = 12, what is p?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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