NumicornNumicornLearn, solve, progress

Quadratic Equations Introduction Practice Tests

These Grade 9 Math practice tests cover quadratic standard form, coefficients, degree, factoring, the zero-product property, square roots, roots and zeros, parabolas, vertex form, axis of symmetry, intercepts, applications, and the discriminant.

Skills covered

  • Identifying a, b, c, degree, leading coefficient, and standard form
  • Expanding and factoring quadratic expressions
  • Solving quadratic equations by square roots and factoring
  • Reading vertex, intercept, opening, and symmetry information from parabolas
  • Using the discriminant and quadratic models to reason about real solutions

How to use these practice tests

Rewrite the equation in standard form, look for a common factor or recognizable pattern, apply the zero-product property when factoring, and verify each root in the original equation. For graphs, connect the coefficient and vertex form to opening, intercepts, and symmetry.

For more Grade 9 Math practice, return to the Grade 9 Math category.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

2. Test

Grade 9 Quadratic Equations Introduction Practice Tests

Practice Grade 9 Math questions about quadratic standard form, coefficients, factoring, roots, zero-product reasoning, parabolas, vertices, intercepts, and the discriminant.

Choose the best answer. Identify the quadratic structure, select a suitable solving method, use exact forms when needed, and check roots in the original equation.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Factor x2+5x+6x^2+5x+6

Please select an answer first.

Correct answer: A

The correct answer is (x+2)(x+3)(x+2)(x+3).

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The factors 2 and 3 multiply to 6 and add to 5.
  3. Check the result: The correct choice is (x+2)(x+3)(x+2)(x+3).

The factors 2 and 3 multiply to 6 and add to 5.

2. QuestionMultiple choice

Factor x2−7x+12x^2-7x+12

Please select an answer first.

Correct answer: B

The correct answer is (x−3)(x−4)(x-3)(x-4).

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The factors -3 and -4 multiply to 12 and add to -7.
  3. Check the result: The correct choice is (x−3)(x−4)(x-3)(x-4).

The factors -3 and -4 multiply to 12 and add to -7.

3. QuestionMultiple choice

Factor x2−16x^2-16

Please select an answer first.

Correct answer: C

The correct answer is (x−4)(x+4)(x-4)(x+4).

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: This is a difference of squares: x squared - 4 squared = (x - 4)(x + 4).
  3. Check the result: The correct choice is (x−4)(x+4)(x-4)(x+4).

This is a difference of squares: x squared - 4 squared = (x - 4)(x + 4).

4. QuestionMultiple choice

Factor 2x2+8x2x^2+8x

Please select an answer first.

Correct answer: D

The correct answer is 2x(x+4)2x(x+4).

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The greatest common factor is 2x, leaving x + 4.
  3. Check the result: The correct choice is 2x(x+4)2x(x+4).

The greatest common factor is 2x, leaving x + 4.

5. QuestionMultiple choice

Solve x2+5x+6=0x^2+5x+6=0

Please select an answer first.

Correct answer: A

The correct answer is x = -2 or x = -3.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Factor as (x + 2)(x + 3) = 0, so x = -2 or x = -3.
  3. Check the result: The correct choice is x = -2 or x = -3.

Factor as (x + 2)(x + 3) = 0, so x = -2 or x = -3.

6. QuestionMultiple choice

Solve x2−7x+12=0x^2-7x+12=0

Please select an answer first.

Correct answer: B

The correct answer is x = 3 or x = 4.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Factor as (x - 3)(x - 4) = 0, giving roots 3 and 4.
  3. Check the result: The correct choice is x = 3 or x = 4.

Factor as (x - 3)(x - 4) = 0, giving roots 3 and 4.

7. QuestionMultiple choice

Solve x2−9x=0x^2-9x=0

Please select an answer first.

Correct answer: C

The correct answer is x = 0 or x = 9.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Factor x(x - 9) = 0, so the zero-product property gives x = 0 or 9.
  3. Check the result: The correct choice is x = 0 or x = 9.

Factor x(x - 9) = 0, so the zero-product property gives x = 0 or 9.

8. QuestionMultiple choice

Solve 2x2−8=02x^2-8=0

Please select an answer first.

Correct answer: D

The correct answer is x = 2 or x = -2.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Divide by 2 to get x squared = 4, so x = ±2.
  3. Check the result: The correct choice is x = 2 or x = -2.

Divide by 2 to get x squared = 4, so x = ±2.

9. QuestionMultiple choice

Solve (x−5)(x+1)=0(x-5)(x+1)=0

Please select an answer first.

Correct answer: A

The correct answer is x = 5 or x = -1.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Set each factor equal to zero: x - 5 = 0 or x + 1 = 0.
  3. Check the result: The correct choice is x = 5 or x = -1.

Set each factor equal to zero: x - 5 = 0 or x + 1 = 0.

10. QuestionMultiple choice

Factor 3x2−123x^2-12

Please select an answer first.

Correct answer: B

The correct answer is 3(x−2)(x+2)3(x-2)(x+2).

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: First factor out 3, then factor x squared - 4 as a difference of squares.
  3. Check the result: The correct choice is 3(x−2)(x+2)3(x-2)(x+2).

First factor out 3, then factor x squared - 4 as a difference of squares.

Previous testNext test