How do you complete the square for the equation $$x^2 + 12x$$ ?

To complete the square, take half of the coefficient of x (which is 12), square it (resulting in 36), and add it to both sides: $$x^2 + 12x + 36 = 36$$ .

What are the roots of the equation $$2x^2 - 32 = 0$$ ?

The roots are $$x = -4$$ and $$x = 4$$ .

How do you solve the equation $$x^2 + 10x = -9$$ ?

Rearrange to $$x^2 + 10x + 9 = 0$$ and factor to find the roots: $$x = -1$$ and $$x = -9$$ .

What is the vertex form of a quadratic equation?

The vertex form of a quadratic equation is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

What is the axis of symmetry for a quadratic equation?

The axis of symmetry for a quadratic equation in standard form $$ax^2 + bx + c$$ is given by the formula $$x = -\frac{b}{2a}$$ .

How do you derive the quadratic formula from completing the square?

Start with the standard form $$ax^2 + bx + c = 0$$ , divide by a, rearrange, complete the square, and solve for x to derive the quadratic formula.

What is the significance of the coefficient 'a' in a quadratic equation?

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a

What is the relationship between the roots and coefficients 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 can you check if your solutions to a quadratic equation are correct?

Substitute the solutions back into the original equation to verify that both sides are equal.

What is the importance of the constant term 'c' in a quadratic equation?

The constant term 'c' represents the y-intercept of the quadratic function, indicating where the graph intersects the y-axis.

Solving Quadratics by multiple methods 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 methods to solve quadratic equations?

Back

3.

FLASHCARD QUESTION

Front

How do you factor a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

5.

FLASHCARD QUESTION

Front

What does the discriminant tell us about a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

Access all questions and much more by creating a free account

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

16 questions

Hand Rules

Flashcard

•

12th Grade

7 questions

Teorías atómicas

Flashcard

•

11th Grade

15 questions

Flashcard - Unit Conversion and Practical Use

Flashcard

•

KG - University

9 questions

matematika kelas xi

Flashcard

•

11th Grade

15 questions

5.4 Costs Flashcards

Flashcard

•

12th Grade

13 questions

Ética Profissional para Desenvolvedores de Software

Flashcard

•

KG - University

10 questions

DNA Flashcards

Flashcard

•

9th - 12th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

54 questions

Analyzing Line Graphs & Tables

Quiz

•

4th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

Discover more resources for Mathematics

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

15 questions

Exponential Growth and Decay Word Problems Practice

Quiz

•

9th - 12th Grade

20 questions

Classifying Polynomials by Degree and Number of Terms

Quiz

•

11th Grade

17 questions

Explore Experimental and Theoretical Probability

Quiz

•

7th - 12th Grade

15 questions

Parallelogram Properties

Quiz

•

10th - 12th Grade

10 questions

Special Right Triangles

Quiz

•

11th Grade

18 questions

Solving Systems- Word Problems

Quiz

•

9th - 12th Grade

34 questions

7.4 Review Cubic and Cube Root Functions

Quiz

•

10th - 12th Grade