What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves and can be found using the formula $$x = -\frac{b}{2a}$$ .

What is the significance of the leading coefficient in a quadratic function?

The leading coefficient (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a

How do you solve a quadratic equation by factoring?

To solve by factoring, rewrite the quadratic in the form $$(x - p)(x - q) = 0$$ , where p and q are the roots, and then set each factor equal to zero.

What is completing the square?

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form $$(x - p)^2 = q$$ , making it easier to solve for x.

What is the relationship between the coefficients and the roots of a quadratic equation?

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

How do you apply the quadratic formula to solve $$x^2 + 6x - 16 = 0$$ ?

Using the quadratic formula, plug in a = 1, b = 6, and c = -16: $$x = \frac{-6 \pm \sqrt{(6)^2 - 4(1)(-16)}}{2(1)}$$ .

What are the roots of the equation $$x^2 - 49 = 0$$ ?

The roots are $$x = -7$$ and $$x = 7$$ , found by factoring as $$(x - 7)(x + 7) = 0$$ .

What does the term 'discriminant' refer to in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root, given by $$D = b^2 - 4ac$$ , which indicates the nature of the roots.

Quadratic Solutions Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

3.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

How do you determine the number of solutions for a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What does it mean if a quadratic equation has no real solutions?

Back

If a quadratic equation has no real solutions, it means that the graph of the quadratic function does not intersect the x-axis, which occurs when the discriminant is negative.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

6.

FLASHCARD QUESTION

Front

How can you find the roots of a quadratic equation graphically?

Back

The roots of a quadratic equation can be found by identifying the x-intercepts of its graph. These are the points where the graph crosses the x-axis.

7.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

Create a free account and access millions of resources

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

10 questions

EARTHQUAKES

Flashcard

•

8th Grade

15 questions

Function Flashcard

Flashcard

•

8th - 12th Grade

11 questions

Climate Change and Its Causes

Flashcard

•

KG

15 questions

Windows Shortcuts

Flashcard

•

7th - 9th Grade

15 questions

S1 Tenses

Flashcard

•

7th - 9th Grade

9 questions

Inequalities

Flashcard

•

9th Grade

10 questions

High Note 2. Unit 1. Test your vocabulary

Flashcard

•

10th Grade

7 questions

Natural Selection and Population Genetics Quiz Review

Flashcard

•

9th Grade

Popular Resources on Wayground

5 questions

This is not a...winter edition (Drawing game)

Quiz

•

1st - 5th Grade

15 questions

4:3 Model Multiplication of Decimals by Whole Numbers

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

10 questions

The Best Christmas Pageant Ever Chapters 1 & 2

Quiz

•

4th Grade

12 questions

Unit 4 Review Day

Quiz

•

3rd Grade

10 questions

Identify Iconic Christmas Movie Scenes

Interactive video

•

6th - 10th Grade

20 questions

Christmas Trivia

Quiz

•

6th - 8th Grade

18 questions

Kids Christmas Trivia

Quiz

•

KG - 5th Grade

Discover more resources for Mathematics

10 questions

Identify Iconic Christmas Movie Scenes

Interactive video

•

6th - 10th Grade

10 questions

Guess the Christmas Movie by the Scene Challenge

Interactive video

•

6th - 10th Grade

20 questions

Triangle Congruence Theorems

Quiz

•

9th Grade

20 questions

Solving One-Step Equations

Quiz

•

6th - 9th Grade

15 questions

Graphing Systems of Equations

Quiz

•

8th - 9th Grade

11 questions

Solve Systems of Equations and Inequalities

Quiz

•

9th - 12th Grade

20 questions

Function or Not a Function

Quiz

•

8th - 9th Grade

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade