Worksheets · Algebra 2

Quadratic inequalities worksheet for Algebra 2

Factor, find where the expression is zero, and those two points cut the number line into three pieces. Test which pieces satisfy the inequality. For a parabola opening upwards, the middle piece is the negative one.

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

Not quite the one you need? Same words, different skill:

Select your difficulty

Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Quadratic Inequalities

Date Period

Solve or graph each inequality. Give solutions in interval notation.

  1. Solve quadratic inequalities

    x2−8x+7≤0
  2. −x2−5x−6≥0
  3. x2+9x+18<0
  4. −x2−2x+15≤0
  5. x2−25≥0
  6. −x2+5x−4<0
  7. x2−2x−15<0
  8. −x2−2x+15<0
  9. x2+9x+20≥0
  10. −x2+1<0

  1. Graph a quadratic inequality

    Graph y≥x2+6x+8−10−10−5−5551010
  2. Graph y≥−x2+3−10−10−5−5551010
  3. Graph y≥−x2+6x−12−10−10−5−5551010
  4. Graph y≤−x2−2x+3−10−10−5−5551010
  5. Graph y≤x2+6x+7−10−10−5−5551010
  6. Graph y≥−x2−2x+4−10−10−5−5551010
  7. Graph y≥x2+2x−10−10−5−5551010
  8. Graph y≥−x2−6x−14−10−10−5−5551010
  9. Graph y≤−x2−4x−8−10−10−5−5551010
  10. Graph y≥−x2−4x−10−10−5−5551010

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

Sigma Prep · sigmaprep.io/worksheets

Name

Quadratic InequalitiesAnswer keyVersion 1

Date Period

Solve or graph each inequality. Give solutions in interval notation.

  1. Solve quadratic inequalities

    x2−8x+7≤0[1,7]
  2. −x2−5x−6≥0[−3,−2]
  3. x2+9x+18<0(−6,−3)
  4. −x2−2x+15≤0(−∞,−5]∪[3,∞)
  5. x2−25≥0(−∞,−5]∪[5,∞)
  6. −x2+5x−4<0(−∞,1)∪(4,∞)
  7. x2−2x−15<0(−3,5)
  8. −x2−2x+15<0(−∞,−5)∪(3,∞)
  9. x2+9x+20≥0(−∞,−5]∪[−4,∞)
  10. −x2+1<0(−∞,−1)∪(1,∞)

  1. Graph a quadratic inequality

    Graph y≥x2+6x+8−10−10−5−5510105Solid parabola, vertex (−3,−1), shade above
  2. Graph y≥−x2+3−10−10−5−5551010Solid parabola, vertex (0,3), shade above
  3. Graph y≥−x2+6x−12−10−10−5−5551010Solid parabola, vertex (3,−3), shade above
  4. Graph y≤−x2−2x+3−10−10−5−5551010Solid parabola, vertex (−1,4), shade below
  5. Graph y≤x2+6x+7−10−10−5−5510105Solid parabola, vertex (−3,−2), shade below
  6. Graph y≥−x2−2x+4−10−10−5−551010Solid parabola, vertex (−1,5), shade above
  7. Graph y≥x2+2x−10−10−5−5551010Solid parabola, vertex (−1,−1), shade above
  8. Graph y≥−x2−6x−14−10−5−5551010−10Solid parabola, vertex (−3,−5), shade above
  9. Graph y≤−x2−4x−8−10−10−5551010−5Solid parabola, vertex (−2,−4), shade below
  10. Graph y≥−x2−4x−10−10−5−5551010Solid parabola, vertex (−2,4), shade above

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

How to do these

(x−2)(x+3)>0

  1. The zeros are 2 and -3.
  2. Opening upwards, the middle piece is negative.
  3. So the outside pieces work.

The answer is (−∞,−3)∪(2,∞).

Where students go wrong

Writing the answer as one interval between the roots when the inequality wants the outside. Sketch the parabola: above the axis is the two outer pieces, below is the middle one.

Also called solving quadratic inequalities or parabola above the axis.

What you can put on this worksheet

Quadratic inequalities
(x−3)(x−1)<0 → (1,3)
Graph y < ax² + bx + c
Graph y≥x2−3 → Solid parabola, vertex (0,−3), shade above
Name a point that works
Name one point that satisfies y<x2+x+1 → e.g. (0,−3)

Questions about these worksheets

Yes. Every quadratic inequalities 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 quadratic inequalities 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 3: quadratic inequalities, graph y < ax² + bx + c and name a point that works. Tick as many as you want and set how many of each, or let it spread them evenly.

Writing the answer as one interval between the roots when the inequality wants the outside. Sketch the parabola: above the axis is the two outer pieces, below is the middle one.