Worksheets · Algebra 2

Writing quadratic functions worksheet for Algebra 2

Algebra 2 writes quadratics from more kinds of information: the vertex and a point, the x-intercepts and a point, or three points that need a system. Choose the form that matches what you were given, then find a.

Also taught in Algebra 1 and Precalculus, each 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.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Writing Quadratic Functions

Date Period

Write the equation of each parabola.

  1. Write a parabola from vertex and point

    Write the equation, in vertex form, of the parabola with vertex (3,−3) that passes through (1,5).
  2. Write the equation, in vertex form, of the parabola with vertex (6,−1) that passes through (9,−10).
  3. Write the equation, in vertex form, of the parabola with vertex (−3,1) that passes through (−2,0).
  4. Write the equation, in vertex form, of the parabola with vertex (2,0) that passes through (0,8).
  5. Write the equation, in vertex form, of the parabola with vertex (−3,−6) that passes through (−4,−4).

  1. Write a parabola from xx-intercepts and point

    Write the equation, in factored form, of the parabola with x-intercepts −4 and −1 that passes through (4,40).
  2. Write the equation, in factored form, of the parabola with x-intercepts −2 and −6 that passes through (0,−12).
  3. Write the equation, in factored form, of the parabola with x-intercepts 0 and −2 that passes through (2,−8).
  4. Write the equation, in factored form, of the parabola with x-intercepts 3 and 4 that passes through (−2,−60).
  5. Write the equation, in factored form, of the parabola with x-intercepts 4 and −3 that passes through (−5,18).

  1. Write a parabola through three points

    Write the equation, in standard form, of the parabola that passes through (−4,6), (0,−2) and (4,22).
  2. Write the equation, in standard form, of the parabola that passes through (−4,−3), (0,5) and (4,45).
  3. Write the equation, in standard form, of the parabola that passes through (0,7), (3,7) and (4,11).
  4. Write the equation, in standard form, of the parabola that passes through (−1,−4), (0,−3) and (3,12).
  5. Write the equation, in standard form, of the parabola that passes through (−3,21), (−2,10) and (0,−6).

  1. Write vertex form from a graph

    Write the equation of the parabola in vertex form.−10−10−5−5551010
  2. Write the equation of the parabola in vertex form.−10−10−5−5551010
  3. Write the equation of the parabola in vertex form.−10−10−5−5551010
  4. Write the equation of the parabola in vertex form.−10−10−5−5510105
  5. Write the equation of the parabola in vertex form.−10−5551010−10

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

Sigma Prep · sigmaprep.io/worksheets

Name

Writing Quadratic FunctionsAnswer keyVersion 2

Date Period

Write the equation of each parabola.

  1. Write a parabola from vertex and point

    Write the equation, in vertex form, of the parabola with vertex (3,−3) that passes through (1,5).y=2(x−3)2−3
  2. Write the equation, in vertex form, of the parabola with vertex (6,−1) that passes through (9,−10).y=−(x−6)2−1
  3. Write the equation, in vertex form, of the parabola with vertex (−3,1) that passes through (−2,0).y=−(x+3)2+1
  4. Write the equation, in vertex form, of the parabola with vertex (2,0) that passes through (0,8).y=2(x−2)2
  5. Write the equation, in vertex form, of the parabola with vertex (−3,−6) that passes through (−4,−4).y=2(x+3)2−6

  1. Write a parabola from xx-intercepts and point

    Write the equation, in factored form, of the parabola with x-intercepts −4 and −1 that passes through (4,40).y=(x+4)(x+1)
  2. Write the equation, in factored form, of the parabola with x-intercepts −2 and −6 that passes through (0,−12).y=−(x+2)(x+6)
  3. Write the equation, in factored form, of the parabola with x-intercepts 0 and −2 that passes through (2,−8).y=−x(x+2)
  4. Write the equation, in factored form, of the parabola with x-intercepts 3 and 4 that passes through (−2,−60).y=−2(x−3)(x−4)
  5. Write the equation, in factored form, of the parabola with x-intercepts 4 and −3 that passes through (−5,18).y=(x−4)(x+3)

  1. Write a parabola through three points

    Write the equation, in standard form, of the parabola that passes through (−4,6), (0,−2) and (4,22).y=x2+2x−2
  2. Write the equation, in standard form, of the parabola that passes through (−4,−3), (0,5) and (4,45).y=x2+6x+5
  3. Write the equation, in standard form, of the parabola that passes through (0,7), (3,7) and (4,11).y=x2−3x+7
  4. Write the equation, in standard form, of the parabola that passes through (−1,−4), (0,−3) and (3,12).y=x2+2x−3
  5. Write the equation, in standard form, of the parabola that passes through (−3,21), (−2,10) and (0,−6).y=x2−6x−6

  1. Write vertex form from a graph

    Write the equation of the parabola in vertex form.−10−10−5−5551010y=−2(x+4)2−5
  2. Write the equation of the parabola in vertex form.−10−10−5−5551010y=(x−2)2
  3. Write the equation of the parabola in vertex form.−10−10−5−5551010y=−x2−1
  4. Write the equation of the parabola in vertex form.−10−10−5−5510105y=2(x+2)2+1
  5. Write the equation of the parabola in vertex form.−10−5551010−10y=−(x−1)2−4

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

How to do these

Zeros at −1 and 3, through (1,−8), in standard form

  1. Intercept form: y = a(x + 1)(x - 3).
  2. Put in (1, -8): -8 = a(2)(-2), so a = 2.
  3. Multiply out: 2(x² - 2x - 3).

The answer is y=2x2−4x−6.

Where students go wrong

Forgetting to find a. A parabola through the right zeros can still be the wrong one; the extra point fixes how wide it opens.

Also called equation of a parabola, quadratic from intercepts, quadratic through three points or writing quadratics.

What you can put on this worksheet

From the vertex and a point
Write the equation, in vertex form, of the parabola with vertex (0,1) that passes through (1,−1). → y=−2x2+1
From the x-intercepts and a point
Write the equation, in factored form, of the parabola with x-intercepts 0 and 1 that passes through (3,6). → y=x(x−1)
From three points
Write the equation, in standard form, of the parabola that passes through (−4,17), (0,1) and (2,5). → y=x2+1
Write the equation from a graph
Write the equation of the parabola in vertex form. → y=2(x−1)2+3
From a graph, opening up or down
Find the equation of the parabola shown. → y=−(x−3)2

Questions about these worksheets

Yes. Every writing quadratic functions 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 writing quadratic functions 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 5: from the vertex and a point, from the x-intercepts and a point, from three points, write the equation from a graph and from a graph, opening up or down. Tick as many as you want and set how many of each, or let it spread them evenly.

Forgetting a. Both y = (x - 2)(x + 3) and y = 2(x - 2)(x + 3) have the same intercepts; only the extra point decides which.