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

5. 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 discriminant of ax2+bx+c=0ax^2+bx+c=0?

Please select an answer first.

Correct answer: A

The correct answer is b2−4acb^2-4ac.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The discriminant is the expression b squared minus 4ac under the square root in the quadratic formula.
  3. Check the result: The correct choice is b2−4acb^2-4ac.

The discriminant is the expression b squared minus 4ac under the square root in the quadratic formula.

2. QuestionMultiple choice

What is the discriminant of x2+4x+4=0x^2+4x+4=0?

Please select an answer first.

Correct answer: B

The correct answer is 0.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Here a = 1, b = 4, c = 4, so b squared - 4ac = 16 - 16 = 0.
  3. Check the result: The correct choice is 0.

Here a = 1, b = 4, c = 4, so b squared - 4ac = 16 - 16 = 0.

3. QuestionMultiple choice

What does the equation x2+1=0x^2+1=0 have?

Please select an answer first.

Correct answer: C

The correct answer is No real solutions..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Its discriminant is -4, which is negative, so it has no real roots.
  3. Check the result: The correct choice is No real solutions..

Its discriminant is -4, which is negative, so it has no real roots.

4. QuestionMultiple choice

How many real solutions does x2−5x+6=0x^2-5x+6=0 have?

Please select an answer first.

Correct answer: D

The correct answer is Two real solutions..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The discriminant is 25 - 24 = 1, which is positive, so there are two real solutions.
  3. Check the result: The correct choice is Two real solutions..

The discriminant is 25 - 24 = 1, which is positive, so there are two real solutions.

5. QuestionMultiple choice

If a is positive in y=ax2+bx+cy=ax^2+bx+c, which way does the parabola open?

Please select an answer first.

Correct answer: A

The correct answer is Upward..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The sign of the leading coefficient determines the opening; positive a means upward.
  3. Check the result: The correct choice is Upward..

The sign of the leading coefficient determines the opening; positive a means upward.

6. QuestionMultiple choice

If a quadratic is written as (x−2)(x+5)=0(x-2)(x+5)=0, what are its roots?

Please select an answer first.

Correct answer: B

The correct answer is 2 and -5.

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

Set each factor to zero: x - 2 = 0 gives 2, and x + 5 = 0 gives -5.

7. QuestionMultiple choice

What number should be added to x2+6xx^2+6x to complete the square?

Please select an answer first.

Correct answer: C

The correct answer is 9.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Take half of 6 and square it: (6/2) squared = 9.
  3. Check the result: The correct choice is 9.

Take half of 6 and square it: (6/2) squared = 9.

8. QuestionMultiple choice

Solve x2−4x−5=0x^2-4x-5=0

Please select an answer first.

Correct answer: D

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: Factor as (x - 5)(x + 1) = 0, giving x = 5 or -1.
  3. Check the result: The correct choice is x = 5 or x = -1.

Factor as (x - 5)(x + 1) = 0, giving x = 5 or -1.

9. QuestionMultiple choice

Solve x2+2x−3=0x^2+2x-3=0

Please select an answer first.

Correct answer: A

The correct answer is x = 1 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 + 3)(x - 1) = 0, so the roots are -3 and 1.
  3. Check the result: The correct choice is x = 1 or x = -3.

Factor as (x + 3)(x - 1) = 0, so the roots are -3 and 1.

10. QuestionMultiple choice

Which statement best summarizes a quadratic function?

Please select an answer first.

Correct answer: B

The correct answer is Its graph is a parabola and its equation can have up to two real zeros..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: A quadratic has degree 2, a parabolic graph, and may have zero, one, or two real x-intercepts.
  3. Check the result: The correct choice is Its graph is a parabola and its equation can have up to two real zeros..

A quadratic has degree 2, a parabolic graph, and may have zero, one, or two real x-intercepts.

Previous testNext test