Grade 9 · Math · Algebra 1

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

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

Grade 9 Math Worksheet - Building Confidence

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

Esme solves 2x² + 5x - 3 = 0. Here a = 2, b = 5 and c = -3. What is b² - 4ac?
Jun solves x² - 6x + 4 = 0 in pencil. Here a = 1, b = -6 and c = 4. What is b² - 4ac?
Kira's robot solves 3x² - 4x - 2 = 0. Here a = 3, b = -4 and c = -2. What is b² - 4ac?
In math club, Luz solves x² + 9x + 14 = 0. Here a = 1, b = 9 and c = 14. What is b² - 4ac?
5.
Milo's puzzle card shows 5 - 3x + 2x² = 0. Before using the formula, write it in order. What are a, b and c?
- a = 2, b = -3, c = 5
- a = 5, b = -3, c = 2
- a = 2, b = -3, c = 0
- a = 2, b = 3, c = 5
6.
Noah copies 4x² + 6 = x from the board. Before using the formula, move every term to the left. What are a, b and c?
- a = 4, b = 1, c = 6
- a = 4, b = 0, c = 6
- a = 6, b = -1, c = 4
- a = 4, b = -1, c = 6
7.
Pia's robot reads x² + 9 = 7x. Before using the formula, move every term to the left. What are a, b and c?
- a = 1, b = -7, c = 9
- a = 1, b = 7, c = 9
- a = 0, b = -7, c = 9
- a = 9, b = -7, c = 1
8.
Ren's math book shows 3x - x² + 8 = 0. Before using the formula, write it in order. What are a, b and c?
- a = 0, b = 3, c = 8
- a = 1, b = 3, c = 8
- a = -1, b = 3, c = 8
- a = 3, b = -1, c = 8
9.
Tala checks x² + 2x + 5 = 0. It finds b² - 4ac = 4 - 20 = -16. How many real solutions are there?
- No real solution
- Two real solutions
- One real solution
10.
In math club, Jun checks 9x² + 6x + 1 = 0. It finds b² - 4ac = 36 - 36 = 0. How many real solutions are there?
- No real solution
- Two real solutions
- One real solution

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.

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