Worksheets · Algebra 1

Quadratic formula worksheet

The formula works on every quadratic, including the ones that do not factor. Easy and medium come out whole so students can check themselves; hard leaves the root in, which is the answer a test wants.

Select your difficulty

Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Quadratic Formula

Date Period

Solve each equation with the quadratic formula.

  1. a2−14a−15=0
  2. 3k2+4k−7=0
  3. 4b2+8b+3=0
  4. 3x2+7x+2=0
  5. 2m2+12m+10=0
  6. 4v2+9v−13=0
  7. 3v2+2v−16=0
  8. 4r2+9r−13=0
  9. a2+8a−20=0
  10. 3a2−a−4=0
  11. 3v2+v−2=0
  12. a2−5a−6=0
  13. a2+6a−16=0
  14. 4k2−6k−18=0
  15. 2r2−12r−14=0
  16. 4k2−k−5=0
  17. 3m2−13m+10=0
  18. 4m2+13m−17=0
  19. p2+3p−10=0
  20. 3k2+11k−14=0

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Quadratic FormulaAnswer keyVersion 1

Date Period

Solve each equation with the quadratic formula.

  1. a2−14a−15=0{15,−1}
  2. 3k2+4k−7=0{1,−73}
  3. 4b2+8b+3=0{−12,−32}
  4. 3x2+7x+2=0{−13,−2}
  5. 2m2+12m+10=0{−1,−5}
  6. 4v2+9v−13=0{1,−134}
  7. 3v2+2v−16=0{2,−83}
  8. 4r2+9r−13=0{1,−134}
  9. a2+8a−20=0{2,−10}
  10. 3a2−a−4=0{43,−1}
  11. 3v2+v−2=0{23,−1}
  12. a2−5a−6=0{6,−1}
  13. a2+6a−16=0{2,−8}
  14. 4k2−6k−18=0{3,−32}
  15. 2r2−12r−14=0{7,−1}
  16. 4k2−k−5=0{54,−1}
  17. 3m2−13m+10=0{103,1}
  18. 4m2+13m−17=0{1,−174}
  19. p2+3p−10=0{2,−5}
  20. 3k2+11k−14=0{1,−143}

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

How to do these

2x2+7x+3=0

  1. a = 2, b = 7, c = 3.
  2. The discriminant is 7² - 4(2)(3) = 25.
  3. x = (-7 ± 5) / 4.

The answer is x=−12 or x=−3.

Where students go wrong

Dividing only part of the top by 2a. The whole numerator goes over the bottom, so (-7 ± 5)/4 is not -7 ± 5/4. The other one is the sign of b when b is already negative: in -3x you substitute b = -3, and -b becomes +3.

Also called solving quadratics with the formula or the quadratic equation.

What you can put on this worksheet

Solve with the quadratic formula
v2+5v−6=0 → {1,−6}
Mix in some with no real solution
v2−4v+5=0 → No solution

Questions about these worksheets

Yes. Every quadratic formula 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 1 is usually taken around 8th or 9th 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 quadratic formula 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 2: solve with the quadratic formula and mix in some with no real solution. Tick as many as you want and set how many of each, or let it spread them evenly.

Dividing only part of the top by 2a. The whole numerator goes over the bottom, so (-7 ± 5)/4 is not -7 ± 5/4. The other one is the sign of b when b is already negative: in -3x you substitute b = -3, and -b becomes +3.