Worksheets · Precalculus

Precalculus graphing parabolas worksheet

Precalculus treats the parabola as a conic: every point is the same distance from a focus and a directrix. The work is rewriting the general form as (y - k)² = 4p(x - h) or (x - h)² = 4p(y - k), then reading off p.

Also taught in Algebra 2, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Parabolas

Date Period

Graph each equation, or find what is asked.

  1. Graph y=x2+6-10-10-5-500551010
  2. Find the vertex, focus and directrix of (y+1)2=8(x−2)
  3. Graph y=−x2−5-10-10-5-500551010
  4. Find the vertex, focus and directrix of x2=−4(y+4)
  5. Graph x=−2(y+4)2−3-10-10-5-500551010
  6. Find the vertex, focus and directrix of (y+2)2=−8(x−3)
  7. Graph x=2(y−3)2+1-10-10-5-500551010
  8. Find the vertex, focus and directrix of (x−2)2=−12(y−4)
  9. Graph x=(y−3)2−5-10-10-5-500551010
  10. Find the vertex, focus and directrix of (y+4)2=16(x+3)
  11. Graph y=−(x−5)2-10-10-5-500551010
  12. Find the vertex, focus and directrix of (x−2)2=12(y−4)
  13. Graph x=−(y−2)2−2-10-10-5-500551010
  14. Find the vertex, focus and directrix of (x−4)2=−4(y+2)
  15. Graph x=2(y+2)2+1-10-10-5-500551010
  16. Find the vertex, focus and directrix of (y+3)2=4x
  17. Graph y=−(x−6)2+6-10-10-5-500551010
  18. Find the vertex, focus and directrix of (y+2)2=−12(x+4)
  19. Graph y=−2(x−4)2−4-10-10-5-500551010
  20. Find the vertex, focus and directrix of (x−4)2=−16y

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing ParabolasAnswer keyVersion 1

Date Period

Graph each equation, or find what is asked.

  1. Graph y=x2+6-10-10-5-500551010Vertex (0,6), opens up
  2. Find the vertex, focus and directrix of (y+1)2=8(x−2)Vertex (2,−1), focus (4,−1), directrix x=0
  3. Graph y=−x2−5-10-10-5-500551010Vertex (0,−5), opens down
  4. Find the vertex, focus and directrix of x2=−4(y+4)Vertex (0,−4), focus (0,−5), directrix y=−3
  5. Graph x=−2(y+4)2−3-10-10-5-500551010Vertex (−3,−4), opens left
  6. Find the vertex, focus and directrix of (y+2)2=−8(x−3)Vertex (3,−2), focus (1,−2), directrix x=5
  7. Graph x=2(y−3)2+1-10-10-5-500551010Vertex (1,3), opens right
  8. Find the vertex, focus and directrix of (x−2)2=−12(y−4)Vertex (2,4), focus (2,1), directrix y=7
  9. Graph x=(y−3)2−5-10-10-5-500551010Vertex (−5,3), opens right
  10. Find the vertex, focus and directrix of (y+4)2=16(x+3)Vertex (−3,−4), focus (1,−4), directrix x=−7
  11. Graph y=−(x−5)2-10-10-5-500551010Vertex (5,0), opens down
  12. Find the vertex, focus and directrix of (x−2)2=12(y−4)Vertex (2,4), focus (2,7), directrix y=1
  13. Graph x=−(y−2)2−2-10-10-5-500551010Vertex (−2,2), opens left
  14. Find the vertex, focus and directrix of (x−4)2=−4(y+2)Vertex (4,−2), focus (4,−3), directrix y=−1
  15. Graph x=2(y+2)2+1-10-10-5-500551010Vertex (1,−2), opens right
  16. Find the vertex, focus and directrix of (y+3)2=4xVertex (0,−3), focus (1,−3), directrix x=−1
  17. Graph y=−(x−6)2+6-10-10-5-500551010Vertex (6,6), opens down
  18. Find the vertex, focus and directrix of (y+2)2=−12(x+4)Vertex (−4,−2), focus (−7,−2), directrix x=−1
  19. Graph y=−2(x−4)2−4-10-10-5-500551010Vertex (4,−4), opens down
  20. Find the vertex, focus and directrix of (x−4)2=−16yVertex (4,0), focus (4,−4), directrix y=4

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Find the vertex, focus and directrix of y2−4y−12x−8=0

  1. Complete the square in y: (y - 2)² = 12x + 12 = 12(x + 1).
  2. The vertex is (-1, 2) and 4p = 12, so p = 3.
  3. p is positive and y is squared, so it opens right: the focus is 3 to the right and the directrix 3 to the left.

The answer is Vertex (−1,2), focus (2,2), directrix x=−4.

Where students go wrong

Using 4p as the distance to the focus. The number in front is 4p, so divide it by 4 to get the distance from the vertex to the focus and to the directrix.

Also called plotting parabolas, parabola graphs or sideways parabolas.

What you can put on this worksheet

A parabola
Graph y=−(x−1)2+3 → Vertex (1,3), opens down
From the focus and directrix
Write the equation of the parabola with focus (0,2) and directrix y=0 → y=14x2+1
Focus and directrix from the equation
Find the vertex, focus and directrix of x=112y2 → Vertex (0,0), focus (3,0), directrix x=−3
Vertex with focus or directrix, sideways, intercept form, fractions
Find the length of the latus rectum: y=−(x+6)2−9 → 1

Questions about these worksheets

Yes. Every graphing parabolas sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the graphing parabolas questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: a parabola, from the focus and directrix, focus and directrix from the equation and vertex with focus or directrix, sideways, intercept form, fractions. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading a sideways parabola as an upright one. If the y is squared then x is the subject, and the vertex is written (x, y) with the constant first. The other slip is the sign of the shift inside the parentheses.