Graph ((y - 6)^2)/(9) - x^2/4 = 1

Center (0, 6), opens up and down

Graph ((y + 1)^2)/(4) - ((x - 3)^2)/(9) = 1

Center (3, -1), opens up and down

Graph ((x + 5)^2)/(9) - ((y + 1)^2)/(9) = 1

Center (-5, -1), opens left and right

Graph ((y + 1)^2)/(4) - ((x + 6)^2)/(9) = 1

Center (-6, -1), opens up and down

Graph ((y + 1)^2)/(4) - ((x + 7)^2)/(4) = 1

Center (-7, -1), opens up and down

Graph ((y - 2)^2)/(16) - ((x + 3)^2)/(4) = 1

Center (-3, 2), opens up and down

Graph ((y + 1)^2)/(16) - ((x - 2)^2)/(4) = 1

Center (2, -1), opens up and down

Graph ((x - 3)^2)/(16) - ((y + 4)^2)/(4) = 1

Center (3, -4), opens left and right

Graph ((y - 3)^2)/(9) - ((x + 5)^2)/(4) = 1

Center (-5, 3), opens up and down

Graph ((y - 2)^2)/(4) - ((x + 7)^2)/(4) = 1

Center (-7, 2), opens up and down

Graph ((x - 2)^2)/(4) - ((y + 1)^2)/(16) = 1

Center (2, -1), opens left and right

Graph ((y - 2)^2)/(16) - ((x - 5)^2)/(16) = 1

Center (5, 2), opens up and down

Graph ((y + 5)^2)/(16) - ((x + 4)^2)/(16) = 1

Center (-4, -5), opens up and down

Graph ((y - 5)^2)/(4) - x^2/16 = 1

Center (0, 5), opens up and down

Graph ((y + 4)^2)/(4) - ((x - 5)^2)/(16) = 1

Center (5, -4), opens up and down

Graph ((x + 5)^2)/(4) - ((y + 1)^2)/(9) = 1

Center (-5, -1), opens left and right

Graph ((y + 6)^2)/(9) - x^2/9 = 1

Center (0, -6), opens up and down

Graph ((y + 2)^2)/(16) - ((x + 4)^2)/(4) = 1

Center (-4, -2), opens up and down

Graph ((x - 2)^2)/(4) - ((y - 1)^2)/(4) = 1

Center (2, 1), opens left and right

Graph ((y + 3)^2)/(4) - ((x + 6)^2)/(4) = 1

Center (-6, -3), opens up and down

Worksheets · Algebra 2

Graphing hyperbolas worksheet

Which fraction comes first decides which way a hyperbola opens, and the two numbers underneath give the slopes of the lines it runs alongside. Draw those lines first and the branches have somewhere to go.



Sigma Prep · sigmaprep.io/worksheets Name Graphing Hyperbolas Date Period Graph each equation. Graph $\frac{{(y - 6)}^{2}}{9} - \frac{x^{2}}{4} = 1$ -10-10-5-55510100 Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x - 3)}^{2}}{9} = 1$ -10-10-5-55510100 Graph $\frac{{(x + 5)}^{2}}{9} - \frac{{(y + 1)}^{2}}{9} = 1$ -10-10-5-55510100 Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x + 6)}^{2}}{9} = 1$ -10-10-5-55510100 Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x + 7)}^{2}}{4} = 1$ -10-10-5-55510100 Graph $\frac{{(y - 2)}^{2}}{16} - \frac{{(x + 3)}^{2}}{4} = 1$ -10-10-5-55510100 Graph $\frac{{(y + 1)}^{2}}{16} - \frac{{(x - 2)}^{2}}{4} = 1$ -10-10-5-55510100 Graph $\frac{{(x - 3)}^{2}}{16} - \frac{{(y + 4)}^{2}}{4} = 1$ -10-10-5-55510100 Graph $\frac{{(y - 3)}^{2}}{9} - \frac{{(x + 5)}^{2}}{4} = 1$ -10-10-5-55510100 Graph $\frac{{(y - 2)}^{2}}{4} - \frac{{(x + 7)}^{2}}{4} = 1$ -10-10-5-55510100 Graph $\frac{{(x - 2)}^{2}}{4} - \frac{{(y + 1)}^{2}}{16} = 1$ -10-10-5-55510100 Graph $\frac{{(y - 2)}^{2}}{16} - \frac{{(x - 5)}^{2}}{16} = 1$ -10-10-5-55510100 Graph $\frac{{(y + 5)}^{2}}{16} - \frac{{(x + 4)}^{2}}{16} = 1$ -10-10-5-55510100 Graph $\frac{{(y - 5)}^{2}}{4} - \frac{x^{2}}{16} = 1$ -10-10-5-55510100 Graph $\frac{{(y + 4)}^{2}}{4} - \frac{{(x - 5)}^{2}}{16} = 1$ -10-10-5-55510100 Graph $\frac{{(x + 5)}^{2}}{4} - \frac{{(y + 1)}^{2}}{9} = 1$ -10-10-5-55510100 Graph $\frac{{(y + 6)}^{2}}{9} - \frac{x^{2}}{9} = 1$ -10-10-5-55510100 Graph $\frac{{(y + 2)}^{2}}{16} - \frac{{(x + 4)}^{2}}{4} = 1$ -10-10-5-55510100 Graph $\frac{{(x - 2)}^{2}}{4} - \frac{{(y - 1)}^{2}}{4} = 1$ -10-10-5-55510100 Graph $\frac{{(y + 3)}^{2}}{4} - \frac{{(x + 6)}^{2}}{4} = 1$ -10-10-5-55510100 Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Hyperbolas

Date Period

Graph each equation.

Graph $\frac{{(y - 6)}^{2}}{9} - \frac{x^{2}}{4} = 1$ -10-10-5-55510100
Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x - 3)}^{2}}{9} = 1$ -10-10-5-55510100
Graph $\frac{{(x + 5)}^{2}}{9} - \frac{{(y + 1)}^{2}}{9} = 1$ -10-10-5-55510100
Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x + 6)}^{2}}{9} = 1$ -10-10-5-55510100
Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x + 7)}^{2}}{4} = 1$ -10-10-5-55510100
Graph $\frac{{(y - 2)}^{2}}{16} - \frac{{(x + 3)}^{2}}{4} = 1$ -10-10-5-55510100
Graph $\frac{{(y + 1)}^{2}}{16} - \frac{{(x - 2)}^{2}}{4} = 1$ -10-10-5-55510100
Graph $\frac{{(x - 3)}^{2}}{16} - \frac{{(y + 4)}^{2}}{4} = 1$ -10-10-5-55510100
Graph $\frac{{(y - 3)}^{2}}{9} - \frac{{(x + 5)}^{2}}{4} = 1$ -10-10-5-55510100
Graph $\frac{{(y - 2)}^{2}}{4} - \frac{{(x + 7)}^{2}}{4} = 1$ -10-10-5-55510100
Graph $\frac{{(x - 2)}^{2}}{4} - \frac{{(y + 1)}^{2}}{16} = 1$ -10-10-5-55510100
Graph $\frac{{(y - 2)}^{2}}{16} - \frac{{(x - 5)}^{2}}{16} = 1$ -10-10-5-55510100
Graph $\frac{{(y + 5)}^{2}}{16} - \frac{{(x + 4)}^{2}}{16} = 1$ -10-10-5-55510100
Graph $\frac{{(y - 5)}^{2}}{4} - \frac{x^{2}}{16} = 1$ -10-10-5-55510100
Graph $\frac{{(y + 4)}^{2}}{4} - \frac{{(x - 5)}^{2}}{16} = 1$ -10-10-5-55510100
Graph $\frac{{(x + 5)}^{2}}{4} - \frac{{(y + 1)}^{2}}{9} = 1$ -10-10-5-55510100
Graph $\frac{{(y + 6)}^{2}}{9} - \frac{x^{2}}{9} = 1$ -10-10-5-55510100
Graph $\frac{{(y + 2)}^{2}}{16} - \frac{{(x + 4)}^{2}}{4} = 1$ -10-10-5-55510100
Graph $\frac{{(x - 2)}^{2}}{4} - \frac{{(y - 1)}^{2}}{4} = 1$ -10-10-5-55510100
Graph $\frac{{(y + 3)}^{2}}{4} - \frac{{(x + 6)}^{2}}{4} = 1$ -10-10-5-55510100



Sigma Prep · sigmaprep.io/worksheets Name Graphing HyperbolasAnswer keyVersion 1 Date Period Graph each equation. Graph $\frac{{(y - 6)}^{2}}{9} - \frac{x^{2}}{4} = 1$ -10-10-5-55510100Center $(0, 6)$ , opens up and down Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x - 3)}^{2}}{9} = 1$ -10-10-5-55510100Center $(3, - 1)$ , opens up and down Graph $\frac{{(x + 5)}^{2}}{9} - \frac{{(y + 1)}^{2}}{9} = 1$ -10-10-5-55510100Center $(- 5, - 1)$ , opens left and right Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x + 6)}^{2}}{9} = 1$ -10-10-5-55510100Center $(- 6, - 1)$ , opens up and down Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x + 7)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 7, - 1)$ , opens up and down Graph $\frac{{(y - 2)}^{2}}{16} - \frac{{(x + 3)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 3, 2)$ , opens up and down Graph $\frac{{(y + 1)}^{2}}{16} - \frac{{(x - 2)}^{2}}{4} = 1$ -10-10-5-55510100Center $(2, - 1)$ , opens up and down Graph $\frac{{(x - 3)}^{2}}{16} - \frac{{(y + 4)}^{2}}{4} = 1$ -10-10-5-55510100Center $(3, - 4)$ , opens left and right Graph $\frac{{(y - 3)}^{2}}{9} - \frac{{(x + 5)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 5, 3)$ , opens up and down Graph $\frac{{(y - 2)}^{2}}{4} - \frac{{(x + 7)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 7, 2)$ , opens up and down Graph $\frac{{(x - 2)}^{2}}{4} - \frac{{(y + 1)}^{2}}{16} = 1$ -10-10-5-55510100Center $(2, - 1)$ , opens left and right Graph $\frac{{(y - 2)}^{2}}{16} - \frac{{(x - 5)}^{2}}{16} = 1$ -10-10-5-55510100Center $(5, 2)$ , opens up and down Graph $\frac{{(y + 5)}^{2}}{16} - \frac{{(x + 4)}^{2}}{16} = 1$ -10-10-5-55510100Center $(- 4, - 5)$ , opens up and down Graph $\frac{{(y - 5)}^{2}}{4} - \frac{x^{2}}{16} = 1$ -10-10-5-55510100Center $(0, 5)$ , opens up and down Graph $\frac{{(y + 4)}^{2}}{4} - \frac{{(x - 5)}^{2}}{16} = 1$ -10-10-5-55510100Center $(5, - 4)$ , opens up and down Graph $\frac{{(x + 5)}^{2}}{4} - \frac{{(y + 1)}^{2}}{9} = 1$ -10-10-5-55510100Center $(- 5, - 1)$ , opens left and right Graph $\frac{{(y + 6)}^{2}}{9} - \frac{x^{2}}{9} = 1$ -10-10-5-55510100Center $(0, - 6)$ , opens up and down Graph $\frac{{(y + 2)}^{2}}{16} - \frac{{(x + 4)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 4, - 2)$ , opens up and down Graph $\frac{{(x - 2)}^{2}}{4} - \frac{{(y - 1)}^{2}}{4} = 1$ -10-10-5-55510100Center $(2, 1)$ , opens left and right Graph $\frac{{(y + 3)}^{2}}{4} - \frac{{(x + 6)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 6, - 3)$ , opens up and down Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing HyperbolasAnswer keyVersion 1

Date Period

Graph each equation.

Graph $\frac{{(y - 6)}^{2}}{9} - \frac{x^{2}}{4} = 1$ -10-10-5-55510100Center $(0, 6)$ , opens up and down
Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x - 3)}^{2}}{9} = 1$ -10-10-5-55510100Center $(3, - 1)$ , opens up and down
Graph $\frac{{(x + 5)}^{2}}{9} - \frac{{(y + 1)}^{2}}{9} = 1$ -10-10-5-55510100Center $(- 5, - 1)$ , opens left and right
Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x + 6)}^{2}}{9} = 1$ -10-10-5-55510100Center $(- 6, - 1)$ , opens up and down
Graph $\frac{{(y + 1)}^{2}}{4} - \frac{{(x + 7)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 7, - 1)$ , opens up and down
Graph $\frac{{(y - 2)}^{2}}{16} - \frac{{(x + 3)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 3, 2)$ , opens up and down
Graph $\frac{{(y + 1)}^{2}}{16} - \frac{{(x - 2)}^{2}}{4} = 1$ -10-10-5-55510100Center $(2, - 1)$ , opens up and down
Graph $\frac{{(x - 3)}^{2}}{16} - \frac{{(y + 4)}^{2}}{4} = 1$ -10-10-5-55510100Center $(3, - 4)$ , opens left and right
Graph $\frac{{(y - 3)}^{2}}{9} - \frac{{(x + 5)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 5, 3)$ , opens up and down
Graph $\frac{{(y - 2)}^{2}}{4} - \frac{{(x + 7)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 7, 2)$ , opens up and down
Graph $\frac{{(x - 2)}^{2}}{4} - \frac{{(y + 1)}^{2}}{16} = 1$ -10-10-5-55510100Center $(2, - 1)$ , opens left and right
Graph $\frac{{(y - 2)}^{2}}{16} - \frac{{(x - 5)}^{2}}{16} = 1$ -10-10-5-55510100Center $(5, 2)$ , opens up and down
Graph $\frac{{(y + 5)}^{2}}{16} - \frac{{(x + 4)}^{2}}{16} = 1$ -10-10-5-55510100Center $(- 4, - 5)$ , opens up and down
Graph $\frac{{(y - 5)}^{2}}{4} - \frac{x^{2}}{16} = 1$ -10-10-5-55510100Center $(0, 5)$ , opens up and down
Graph $\frac{{(y + 4)}^{2}}{4} - \frac{{(x - 5)}^{2}}{16} = 1$ -10-10-5-55510100Center $(5, - 4)$ , opens up and down
Graph $\frac{{(x + 5)}^{2}}{4} - \frac{{(y + 1)}^{2}}{9} = 1$ -10-10-5-55510100Center $(- 5, - 1)$ , opens left and right
Graph $\frac{{(y + 6)}^{2}}{9} - \frac{x^{2}}{9} = 1$ -10-10-5-55510100Center $(0, - 6)$ , opens up and down
Graph $\frac{{(y + 2)}^{2}}{16} - \frac{{(x + 4)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 4, - 2)$ , opens up and down
Graph $\frac{{(x - 2)}^{2}}{4} - \frac{{(y - 1)}^{2}}{4} = 1$ -10-10-5-55510100Center $(2, 1)$ , opens left and right
Graph $\frac{{(y + 3)}^{2}}{4} - \frac{{(x + 6)}^{2}}{4} = 1$ -10-10-5-55510100Center $(- 6, - 3)$ , opens up and down

How to do these

Graph $\frac{{(x + 1)}^{2}}{9} - \frac{{(y - 2)}^{2}}{4} = 1$

The x term is first, so it opens left and right.
The center is at (-1, 2), with vertices 3 either side.
The asymptotes run out from the center with slopes of plus and minus two thirds.

The answer is Center $(- 1, 2)$ , opens left and right.

Where students go wrong

Opening it the wrong way. It opens towards whichever variable is positive, not towards the larger number. The other slip is drawing the branches without the asymptotes, which is what makes the shape come out right.

Also called plotting hyperbolas, hyperbola graphs or asymptotes of a hyperbola.

Questions about these worksheets

Yes. Every graphing hyperbolas 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.

Algebra 2 is usually taken around 10th or 11th 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 hyperbolas 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 three 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.

Graphing hyperbolas worksheet

Graphing Hyperbolas

Graphing HyperbolasAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

Are these graphing hyperbolas worksheets free?+

Do the graphing hyperbolas worksheets come with an answer key?+

Are these graphing hyperbolas worksheets printable?+

What grade are these graphing hyperbolas worksheets for?+

Can I get a different version of the same graphing hyperbolas worksheet?+

Is this a free alternative to Kuta Software for graphing hyperbolas?+

Can I choose how hard the graphing hyperbolas questions are?+

What do students get wrong with graphing hyperbolas?+