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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.

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

1. 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

What is the degree of a quadratic equation?

Please select an answer first.

Correct answer: A

The correct answer is 2.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: A quadratic equation has a highest variable exponent of 2.
  3. Check the result: The correct choice is 2.

A quadratic equation has a highest variable exponent of 2.

2. QuestionMultiple choice

In standard form ax2+bx+c=0ax^2+bx+c=0, what is a for 3x2−2x+5=03x^2-2x+5=0?

Please select an answer first.

Correct answer: B

The correct answer is 3.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The coefficient of x squared is a, so a = 3.
  3. Check the result: The correct choice is 3.

The coefficient of x squared is a, so a = 3.

3. QuestionMultiple choice

In −x2+4x−7=0-x^2+4x-7=0, what is c?

Please select an answer first.

Correct answer: C

The correct answer is -7.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The constant term is c, and the constant in the equation is -7.
  3. Check the result: The correct choice is -7.

The constant term is c, and the constant in the equation is -7.

4. QuestionMultiple choice

What is the leading coefficient of 2x2−9x+12x^2-9x+1?

Please select an answer first.

Correct answer: D

The correct answer is 2.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The leading term is 2x squared, so its coefficient is 2.
  3. Check the result: The correct choice is 2.

The leading term is 2x squared, so its coefficient is 2.

5. QuestionMultiple choice

Which expression is quadratic?

Please select an answer first.

Correct answer: A

The correct answer is x2−5x+6x^2-5x+6.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The expression has degree 2 because its highest exponent is x squared.
  3. Check the result: The correct choice is x2−5x+6x^2-5x+6.

The expression has degree 2 because its highest exponent is x squared.

6. QuestionMultiple choice

Expand (x+3)2(x+3)^2

Please select an answer first.

Correct answer: B

The correct answer is x2+6x+9x^2+6x+9.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Use the square pattern: x squared + 2(3)x + 3 squared.
  3. Check the result: The correct choice is x2+6x+9x^2+6x+9.

Use the square pattern: x squared + 2(3)x + 3 squared.

7. QuestionMultiple choice

Solve x2=25x^2=25

Please select an answer first.

Correct answer: C

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

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Both 5 squared and -5 squared equal 25, so there are two real solutions.
  3. Check the result: The correct choice is x = 5 or x = -5.

Both 5 squared and -5 squared equal 25, so there are two real solutions.

8. QuestionMultiple choice

Solve x2−9=0x^2-9=0

Please select an answer first.

Correct answer: D

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

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Add 9 to get x squared = 9, so x = ±3.
  3. Check the result: The correct choice is x = 3 or x = -3.

Add 9 to get x squared = 9, so x = ±3.

9. QuestionMultiple choice

Solve x(x−4)=0x(x-4)=0

Please select an answer first.

Correct answer: A

The correct answer is x = 0 or x = 4.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: By the zero-product property, x = 0 or x - 4 = 0, giving x = 0 or 4.
  3. Check the result: The correct choice is x = 0 or x = 4.

By the zero-product property, x = 0 or x - 4 = 0, giving x = 0 or 4.

10. QuestionMultiple choice

Write 4x−2x2+14x-2x^2+1 in standard quadratic form.

Please select an answer first.

Correct answer: B

The correct answer is −2x2+4x+1-2x^2+4x+1.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Arrange the terms in descending powers of x: -2x squared + 4x + 1.
  3. Check the result: The correct choice is −2x2+4x+1-2x^2+4x+1.

Arrange the terms in descending powers of x: -2x squared + 4x + 1.

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