Grade 9 · Math · Algebra 1

9th grade The quadratic formula, and the discriminant: how many real solutions worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

The quadratic formula, and the discriminant: how many real solutions

Grade 9 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Kira solves 2x² + 7x - 15 = 0 with the quadratic formula. What is the larger solution?
Luz's robot uses the formula on 2x² - 13x - 15 = 0. What is the larger solution?
Milo solves 3x² - 13x - 10 = 0 with the formula, step by step. What is the smaller solution?
4.
Pia checks 2x² + 3x + 5 = 0 before solving. How many real solutions does it have?
- Two real solutions
- No real solution
- One real solution
5.
Ren's robot checks x² - 10x + 25 = 0. How many real solutions does it have?
- Two real solutions
- One real solution
- No real solution
6.
In math club, Zee checks 4x² + 4x + 1 = 0. How many real solutions does it have?
- No real solution
- One real solution
- Two real solutions
Esme solves x² + 4x - 7 = 0 with the formula. What is the positive solution, to the nearest tenth?
Jun's robot solves 2x² - 5x - 1 = 0 and rounds at the end. What is the positive solution, to the nearest tenth?
Kira solves 3x² + 2x - 4 = 0 in pencil. What is the negative solution, to the nearest tenth?
In math club, Luz solves x² - 8x + 5 = 0. What is the smaller solution, to the nearest tenth?

The quadratic formula, and the discriminant: how many real solutions. Every version has 10 questions, and the answer key prints on the second page.

Standard: A-REI.B.4b

quadratic formula: x = (-b ± √(b² - 4ac)) ÷ 2a, a recipe for the zero rows.

discriminant: b² - 4ac, the number under the root.

a, b, c: The numbers with x², with x, and alone, after 0 is on one side.

±: Do it twice: once with +, once with -.

real solution: A real number that solves it; a row with output 0.

Your child got the sign of 4ac wrong.

Your child doubled b instead of squaring it.

Your child made b² negative when b was negative.

Ask: when c is negative, is -4ac positive or negative?

Ask: is b² the same as 2 × b?

Ask: what is (-6) × (-6)?

What is the most common mistake with the quadratic formula, and the discriminant: how many real solutions?

Your child got the sign of 4ac wrong.

How can I help my child with the quadratic formula, and the discriminant: how many real solutions?

Ask: when c is negative, is -4ac positive or negative?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records