Worksheets · Algebra 2

Vertex form worksheet for Algebra 2

In Algebra 2 vertex form describes transformations of y = x², and it is how you write a parabola from its vertex and one point. Completing the square turns standard form into vertex form, and expanding turns it back. The vertex is (h, k), with h the opposite of the number in the parentheses.

Also taught in Algebra 1, at its own level and with its own examples.

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Name

Vertex Form of a Parabola

Date Period

Convert between vertex form and standard form, or write the equation.

  1. Write in vertex form

    Complete the square: y=x2−18x+97.
  2. Write in vertex form: y=3x2−6x+16
  3. Write in vertex form: y=x2+9x+18.
  4. Write in vertex form: y=3x2+36x+121
  5. What is the vertex form of y=x2−16x+53?
  6. Write in vertex form: y=−2x2+16x−19
  7. Rewrite y=x2+5x+12 in the form y=(x−h)2+k.
  8. Write in vertex form: y=−x2−8x−4
  9. Find the vertex form of y=x2+14x+60.
  10. Write in vertex form: y=−2x2−24x−64

  1. Write vertex form in standard form

    Write in standard form: y=−(x+7)2−12
  2. Write in standard form: y=2(x+7)2−10
  3. Write in standard form: y=−(x−6)2−11
  4. Write in standard form: y=(x−6)2−10
  5. Write in standard form: y=(x+7)2+11

  1. Write a parabola from vertex and point

    Write the equation, in vertex form, of the parabola with vertex (−4,−1) that passes through (−2,−13).
  2. Write the equation, in vertex form, of the parabola with vertex (3,8) that passes through (1,20).
  3. Write the equation, in vertex form, of the parabola with vertex (−3,9) that passes through (−6,18).
  4. Write the equation, in vertex form, of the parabola with vertex (−2,4) that passes through (0,0).
  5. Write the equation, in vertex form, of the parabola with vertex (1,7) that passes through (−1,3).

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

Sigma Prep · sigmaprep.io/worksheets

Name

Vertex Form of a ParabolaAnswer keyVersion 2

Date Period

Convert between vertex form and standard form, or write the equation.

  1. Write in vertex form

    Complete the square: y=x2−18x+97.y=(x−9)2+16
  2. Write in vertex form: y=3x2−6x+16y=3(x−1)2+13
  3. Write in vertex form: y=x2+9x+18.y=(x+92)2−94
  4. Write in vertex form: y=3x2+36x+121y=3(x+6)2+13
  5. What is the vertex form of y=x2−16x+53?y=(x−8)2−11
  6. Write in vertex form: y=−2x2+16x−19y=−2(x−4)2+13
  7. Rewrite y=x2+5x+12 in the form y=(x−h)2+k.y=(x+52)2+234
  8. Write in vertex form: y=−x2−8x−4y=−(x+4)2+12
  9. Find the vertex form of y=x2+14x+60.y=(x+7)2+11
  10. Write in vertex form: y=−2x2−24x−64y=−2(x+6)2+8

  1. Write vertex form in standard form

    Write in standard form: y=−(x+7)2−12y=−x2−14x−61
  2. Write in standard form: y=2(x+7)2−10y=2x2+28x+88
  3. Write in standard form: y=−(x−6)2−11y=−x2+12x−47
  4. Write in standard form: y=(x−6)2−10y=x2−12x+26
  5. Write in standard form: y=(x+7)2+11y=x2+14x+60

  1. Write a parabola from vertex and point

    Write the equation, in vertex form, of the parabola with vertex (−4,−1) that passes through (−2,−13).y=−3(x+4)2−1
  2. Write the equation, in vertex form, of the parabola with vertex (3,8) that passes through (1,20).y=3(x−3)2+8
  3. Write the equation, in vertex form, of the parabola with vertex (−3,9) that passes through (−6,18).y=(x+3)2+9
  4. Write the equation, in vertex form, of the parabola with vertex (−2,4) that passes through (0,0).y=−(x+2)2+4
  5. Write the equation, in vertex form, of the parabola with vertex (1,7) that passes through (−1,3).y=−(x−1)2+7

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

How to do these

Write y=x2+6x+5 in vertex form

  1. Half of 6 is 3; add and subtract 9.
  2. y = (x² + 6x + 9) - 9 + 5.
  3. Write the perfect square.

The answer is y=(x+3)2−4.

Where students go wrong

Reading the vertex as (3, -4). In y = (x + 3)² - 4 the vertex is (-3, -4): the x-value is the opposite of the number in the parentheses.

Also called vertex form of a quadratic, converting to vertex form or equation from the vertex.

What you can put on this worksheet

Rewrite by completing the square
Find the vertex form of y=x2+10x+20. → y=(x+5)2−5
Vertex form to standard form
Write in standard form: y=(x−3)2+1 → y=x2−6x+10
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
Leading coefficient other than 1
Write in vertex form: y=3x2−30x+62 → y=3(x−5)2−13
From factored form, from an unsolved equation
Write in vertex form: x2+6x+y+17=0 → y=−(x+3)2−8

Questions about these worksheets

Yes. Every vertex form 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 form 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 5: rewrite by completing the square, vertex form to standard form, from the vertex and a point, leading coefficient other than 1 and from factored form, from an unsolved equation. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading the vertex with the wrong sign. In (x - 2)² the vertex is at x = 2, not -2; the form subtracts h.