In Algebra 1 the discriminant tells you how many times a parabola crosses the x-axis before you solve anything. It also answers questions in reverse, like which values of k give one solution or two.
Also taught in Algebra 2, 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.
For what values of kdoes x2+6x+k=0 have two real solutions?
The discriminant is b² - 4ac = 36 - 4k.
Two real solutions need it to be positive: 36 - 4k > 0.
Solve: 4k < 36, so k < 9.
The answer is k<9.
Where students go wrong
Getting the inequality backwards in the k questions. No real solutions needs a negative discriminant: x² + 4x + k = 0 needs 16 - 4k < 0, so k > 4, not k < 4.
Also called the nature of the roots or b squared minus 4ac.
What you can put on this worksheet
Find the discriminant and say what it means
Find the discriminant: v2+7v−6=0→ 73, two irrational solutions
Find the unknown coefficient for a number of solutions
For what value of kdoes x2+6x+k=0 have exactly one real solution?→ k=9
Not in standard form, write one
Find the discriminant and describe the solutions: 3k2−104=4→ D=1296; two real solutions
Questions about these worksheets
Yes. Every discriminant 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 discriminant 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: find the discriminant and say what it means, find the unknown coefficient for a number of solutions and not in standard form, write one. Tick as many as you want and set how many of each, or let it spread them evenly.
Getting the sign of -4ac wrong. b² is never negative, so the sign of the discriminant turns on -4ac: when a and c have opposite signs, -4ac is positive and the discriminant is guaranteed positive.