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 - Challenge Me

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

1.
Pia solves x² - 2x - 11 = 0 exactly, root sign and all. Which gives both exact solutions?
- x = -1 ± 2√3
- x = 1 ± 4√3
- x = 1 ± 2√3
- No real solution
2.
In math club, Ren finds the exact solutions of x² + 8x + 13 = 0. Which gives both exact solutions?
- x = -4 ± 2√3
- x = -4 ± √3
- x = -4 ± √29
- x = 4 ± √3
Tala wants 4x² + 12x + c = 0 to have exactly one solution. What is c?
Zee's robot picks c so that x² - 8x + c = 0 has exactly one solution. What is c?
Esme needs 2x² + 12x + c = 0 to touch the x-axis at one point only. What is c?
In math club, Jun chooses c so 3x² - 18x + c = 0 has exactly one solution. What is c?
Kira solves x² = 4x + 3 with the formula. What is the positive solution, to the nearest tenth?
Luz's robot solves 3x² + 1 = 6x. What is the larger solution, to the nearest tenth?
Milo solves 2x² = 7 - 3x in pencil. What is the positive solution, to the nearest tenth?
In math club, Noah solves x(x + 5) = 3. 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.

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