Find the vertex, focus and directrix of x^2 = -16(y + 3)

Vertex (0, -3), focus (0, -7), directrix y = 1

Find the vertex, focus and directrix of (x - 1)^2 = -4(y - 3)

Vertex (1, 3), focus (1, 2), directrix y = 4

Find the vertex, focus and directrix of (x - 2)^2 = 16(y + 3)

Vertex (2, -3), focus (2, 1), directrix y = -7

Find the vertex, focus and directrix of (x + 2)^2 = 12(y - 2)

Vertex (-2, 2), focus (-2, 5), directrix y = -1

Find the vertex, focus and directrix of (y - 4)^2 = 8x

Vertex (0, 4), focus (2, 4), directrix x = -2

Find the vertex, focus and directrix of (x + 3)^2 = -8(y + 2)

Vertex (-3, -2), focus (-3, -4), directrix y = 0

Find the vertex, focus and directrix of x = 1/12y^2

Vertex (0, 0), focus (3, 0), directrix x = -3

Find the vertex, focus and directrix: y^2 - 2y + 8x + 1 = 0

Vertex (0, 1); Focus (-2, 1); Directrix x = 2

Worksheets · Algebra 2

Vertex of a parabola worksheet for Algebra 2

The vertex is where the parabola turns, and it can be read off once the equation is in vertex form. Completing the square gets you there from any quadratic. The focus and directrix sit p either side of the vertex, where the number in front is 1/(4p).

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

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Vertex of a Parabola Date Period Answer each question. Find the vertex of $y = ax^2 + bx + c$ Find the vertex of $y = 4 x^{2} + 15$ Find the vertex of $y = - 4 x^{2} - 48 x - 144$ Find the vertex of $y = - 4 x^{2} + 24 x - 35$ Find the vertex of $y = 5 x^{2} + 60 x + 173$ Find the vertex of $y = 5 x^{2} - 30 x + 58$ Find the vertex of $y = - 5 x^{2} - 9$ Find the vertex of $y = - 4 x^{2} + 8 x + 4$ Write a parabola from focus and directrix Write the equation of the parabola with focus $(6, 0)$ and directrix $y = - 6$ Write the equation of the parabola with focus $(- 6, 0)$ and directrix $y = - 2$ Write the equation of the parabola with focus $(3, - 2)$ and directrix $y = - 6$ Write the equation of the parabola with focus $(- 6, 3)$ and directrix $y = 1$ Write the equation of the parabola with focus $(4, 5)$ and directrix $y = 7$ Write the equation of the parabola with focus $(- 1, - 2)$ and directrix $y = 4$ Write the equation of the parabola with focus $(- 6, - 8)$ and directrix $y = - 2$ Find the vertex, focus and directrix Find the vertex, focus and directrix of $x^{2} = - 16 (y + 3)$ Find the vertex, focus and directrix of ${(x - 1)}^{2} = - 4 (y - 3)$ Find the vertex, focus and directrix of ${(x - 2)}^{2} = 16 (y + 3)$ Find the vertex, focus and directrix of ${(x + 2)}^{2} = 12 (y - 2)$ Find the vertex, focus and directrix of ${(y - 4)}^{2} = 8 x$ Find the vertex, focus and directrix of ${(x + 3)}^{2} = - 8 (y + 2)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Vertex of a Parabola

Date Period

Answer each question.

Find the vertex of $y = ax^2 + bx + c$
Find the vertex of $y = 4 x^{2} + 15$
Find the vertex of $y = - 4 x^{2} - 48 x - 144$
Find the vertex of $y = - 4 x^{2} + 24 x - 35$
Find the vertex of $y = 5 x^{2} + 60 x + 173$
Find the vertex of $y = 5 x^{2} - 30 x + 58$
Find the vertex of $y = - 5 x^{2} - 9$
Find the vertex of $y = - 4 x^{2} + 8 x + 4$

Write a parabola from focus and directrix
Write the equation of the parabola with focus $(6, 0)$ and directrix $y = - 6$
Write the equation of the parabola with focus $(- 6, 0)$ and directrix $y = - 2$
Write the equation of the parabola with focus $(3, - 2)$ and directrix $y = - 6$
Write the equation of the parabola with focus $(- 6, 3)$ and directrix $y = 1$
Write the equation of the parabola with focus $(4, 5)$ and directrix $y = 7$
Write the equation of the parabola with focus $(- 1, - 2)$ and directrix $y = 4$
Write the equation of the parabola with focus $(- 6, - 8)$ and directrix $y = - 2$

Find the vertex, focus and directrix
Find the vertex, focus and directrix of $x^{2} = - 16 (y + 3)$
Find the vertex, focus and directrix of ${(x - 1)}^{2} = - 4 (y - 3)$
Find the vertex, focus and directrix of ${(x - 2)}^{2} = 16 (y + 3)$
Find the vertex, focus and directrix of ${(x + 2)}^{2} = 12 (y - 2)$
Find the vertex, focus and directrix of ${(y - 4)}^{2} = 8 x$
Find the vertex, focus and directrix of ${(x + 3)}^{2} = - 8 (y + 2)$



Sigma Prep · sigmaprep.io/worksheets Name Vertex of a ParabolaAnswer keyVersion 1 Date Period Answer each question. Find the vertex of $y = ax^2 + bx + c$ Find the vertex of $y = 4 x^{2} + 15$ $(0, 15)$ Find the vertex of $y = - 4 x^{2} - 48 x - 144$ $(- 6, 0)$ Find the vertex of $y = - 4 x^{2} + 24 x - 35$ $(3, 1)$ Find the vertex of $y = 5 x^{2} + 60 x + 173$ $(- 6, - 7)$ Find the vertex of $y = 5 x^{2} - 30 x + 58$ $(3, 13)$ Find the vertex of $y = - 5 x^{2} - 9$ $(0, - 9)$ Find the vertex of $y = - 4 x^{2} + 8 x + 4$ $(1, 8)$ Write a parabola from focus and directrix Write the equation of the parabola with focus $(6, 0)$ and directrix $y = - 6$ $y = \frac{1}{12} {(x - 6)}^{2} - 3$ Write the equation of the parabola with focus $(- 6, 0)$ and directrix $y = - 2$ $y = \frac{1}{4} {(x + 6)}^{2} - 1$ Write the equation of the parabola with focus $(3, - 2)$ and directrix $y = - 6$ $y = \frac{1}{8} {(x - 3)}^{2} - 4$ Write the equation of the parabola with focus $(- 6, 3)$ and directrix $y = 1$ $y = \frac{1}{4} {(x + 6)}^{2} + 2$ Write the equation of the parabola with focus $(4, 5)$ and directrix $y = 7$ $y = - \frac{1}{4} {(x - 4)}^{2} + 6$ Write the equation of the parabola with focus $(- 1, - 2)$ and directrix $y = 4$ $y = - \frac{1}{12} {(x + 1)}^{2} + 1$ Write the equation of the parabola with focus $(- 6, - 8)$ and directrix $y = - 2$ $y = - \frac{1}{12} {(x + 6)}^{2} - 5$ Find the vertex, focus and directrix Find the vertex, focus and directrix of $x^{2} = - 16 (y + 3)$ Vertex $(0, - 3)$ , focus $(0, - 7)$ , directrix $y = 1$ Find the vertex, focus and directrix of ${(x - 1)}^{2} = - 4 (y - 3)$ Vertex $(1, 3)$ , focus $(1, 2)$ , directrix $y = 4$ Find the vertex, focus and directrix of ${(x - 2)}^{2} = 16 (y + 3)$ Vertex $(2, - 3)$ , focus $(2, 1)$ , directrix $y = - 7$ Find the vertex, focus and directrix of ${(x + 2)}^{2} = 12 (y - 2)$ Vertex $(- 2, 2)$ , focus $(- 2, 5)$ , directrix $y = - 1$ Find the vertex, focus and directrix of ${(y - 4)}^{2} = 8 x$ Vertex $(0, 4)$ , focus $(2, 4)$ , directrix $x = - 2$ Find the vertex, focus and directrix of ${(x + 3)}^{2} = - 8 (y + 2)$ Vertex $(- 3, - 2)$ , focus $(- 3, - 4)$ , directrix $y = 0$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Vertex of a ParabolaAnswer keyVersion 1

Date Period

Answer each question.

Find the vertex of $y = ax^2 + bx + c$
Find the vertex of $y = 4 x^{2} + 15$ $(0, 15)$
Find the vertex of $y = - 4 x^{2} - 48 x - 144$ $(- 6, 0)$
Find the vertex of $y = - 4 x^{2} + 24 x - 35$ $(3, 1)$
Find the vertex of $y = 5 x^{2} + 60 x + 173$ $(- 6, - 7)$
Find the vertex of $y = 5 x^{2} - 30 x + 58$ $(3, 13)$
Find the vertex of $y = - 5 x^{2} - 9$ $(0, - 9)$
Find the vertex of $y = - 4 x^{2} + 8 x + 4$ $(1, 8)$

Write a parabola from focus and directrix
Write the equation of the parabola with focus $(6, 0)$ and directrix $y = - 6$ $y = \frac{1}{12} {(x - 6)}^{2} - 3$
Write the equation of the parabola with focus $(- 6, 0)$ and directrix $y = - 2$ $y = \frac{1}{4} {(x + 6)}^{2} - 1$
Write the equation of the parabola with focus $(3, - 2)$ and directrix $y = - 6$ $y = \frac{1}{8} {(x - 3)}^{2} - 4$
Write the equation of the parabola with focus $(- 6, 3)$ and directrix $y = 1$ $y = \frac{1}{4} {(x + 6)}^{2} + 2$
Write the equation of the parabola with focus $(4, 5)$ and directrix $y = 7$ $y = - \frac{1}{4} {(x - 4)}^{2} + 6$
Write the equation of the parabola with focus $(- 1, - 2)$ and directrix $y = 4$ $y = - \frac{1}{12} {(x + 1)}^{2} + 1$
Write the equation of the parabola with focus $(- 6, - 8)$ and directrix $y = - 2$ $y = - \frac{1}{12} {(x + 6)}^{2} - 5$

Find the vertex, focus and directrix
Find the vertex, focus and directrix of $x^{2} = - 16 (y + 3)$ Vertex $(0, - 3)$ , focus $(0, - 7)$ , directrix $y = 1$
Find the vertex, focus and directrix of ${(x - 1)}^{2} = - 4 (y - 3)$ Vertex $(1, 3)$ , focus $(1, 2)$ , directrix $y = 4$
Find the vertex, focus and directrix of ${(x - 2)}^{2} = 16 (y + 3)$ Vertex $(2, - 3)$ , focus $(2, 1)$ , directrix $y = - 7$
Find the vertex, focus and directrix of ${(x + 2)}^{2} = 12 (y - 2)$ Vertex $(- 2, 2)$ , focus $(- 2, 5)$ , directrix $y = - 1$
Find the vertex, focus and directrix of ${(y - 4)}^{2} = 8 x$ Vertex $(0, 4)$ , focus $(2, 4)$ , directrix $x = - 2$
Find the vertex, focus and directrix of ${(x + 3)}^{2} = - 8 (y + 2)$ Vertex $(- 3, - 2)$ , focus $(- 3, - 4)$ , directrix $y = 0$

How to do these

Find the vertex of $y = 2 x^{2} - 12 x + 13$

x = -b/(2a) = 12/4 = 3.
Put 3 back in to get y.
2(9) - 36 + 13 = -5.

The answer is $(3, - 5)$ .

Where students go wrong

Reading the vertex straight off the standard form. In y = 2x² - 12x + 13 the vertex is not (12, 13) or (-12, 13); the equation has to be rearranged before anything can be read from it.

Also called finding the vertex or axis of symmetry.

What you can put on this worksheet

Find the vertex: Find the vertex of $y = 2 x^{2} - 12 x + 10$ → $(3, - 8)$
From the focus and directrix: Write the equation of the parabola with focus $(0, 2)$ and directrix $y = 0$ → $y = \frac{1}{4} x^{2} + 1$
Focus and directrix from the equation: Find the vertex, focus and directrix of $x = \frac{1}{12} y^{2}$ → Vertex $(0, 0)$ , focus $(3, 0)$ , directrix $x = - 3$
Sideways, from general form: Find the vertex, focus and directrix: $y^{2} - 2 y + 8 x + 1 = 0$ → Vertex $(0, 1)$
Focus $(- 2, 1)$
Directrix $x = 2$
Vertex and a fractional directrix: Write the equation of the parabola with vertex $(0, 1)$ and directrix $y = \frac{7}{4}$ → $y = - \frac{1}{3} x^{2} + 1$
Vertex and an x-intercept: Write the equation, in vertex form, of the parabola with an $x$ -intercept at $3$ and vertex $(0, 18)$ → $y = - 2 x^{2} + 18$

Questions about these worksheets

Yes. Every vertex of a parabola 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 vertex of a parabola 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.

You pick from 6: find the vertex, from the focus and directrix, focus and directrix from the equation, sideways, from general form, vertex and a fractional directrix and vertex and an x-intercept. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading the vertex straight off the standard form. In y = 2x² - 12x + 13 the vertex is not (12, 13) or (-12, 13); the equation has to be rearranged before anything can be read from it.

Vertex of a parabola worksheet for Algebra 2

Select your difficulty

Find the vertex of y=ax2+bx+cy = ax^2 + bx + cy=ax2+bx+c

Write a parabola from focus and directrix

Find the vertex, focus and directrix

Find the vertex of y=ax2+bx+cy = ax^2 + bx + cy=ax2+bx+c

Write a parabola from focus and directrix

Find the vertex, focus and directrix

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these vertex of a parabola worksheets free?+

Do the vertex of a parabola worksheets come with an answer key?+

Are these vertex of a parabola worksheets printable?+

What grade are these vertex of a parabola worksheets for?+

Can I get a different version of the same vertex of a parabola worksheet?+

Is this a free alternative to Kuta Software for vertex of a parabola?+

Can I choose how hard the vertex of a parabola questions are?+

What kinds of question are on a vertex of a parabola worksheet?+

What do students get wrong with vertex of a parabola?+

Find the vertex of $y = ax^2 + bx + c$

Find the vertex of $y = ax^2 + bx + c$