Solve the quadratic equation: $$2r^2 - 3r - 5 = 0$$

Using the quadratic formula, the solutions are $$r = \frac{{3 \\pm \text{sqrt}(49)}}{{4}} = \frac{{3 \\pm 7}}{{4}}$$ , which gives $$r = 5/2, -1$$ .

Solve the quadratic equation: $$2x^2 - 4x + 7 = 0$$

Using the quadratic formula, the solutions are $$x = \frac{{4 \\pm \text{sqrt}(-24)}}{{4}} = \frac{{4 \\pm 2i\text{sqrt}(6)}}{{4}} = \frac{{2 \\pm i\text{sqrt}(10)}}{{2}}$$ .

Solve the quadratic equation: $$x^2 - 6x + 4 = 0$$

Using the quadratic formula, the solutions are $$x = \frac{{6 \\pm \text{sqrt}(20)}}{{2}} = 3 \\pm \text{sqrt}(5)$$ .

Solve the quadratic equation: $$2x^2 + 2x + 12 = 0$$

Using the quadratic formula, the solutions are $$x = \frac{{-2 \\pm \text{sqrt}(-88)}}{{4}} = \frac{{-2 \\pm 2i\text{sqrt}(22)}}{{4}} = \frac{{-1 \\pm i\text{sqrt}(23)}}{{2}}$$ .

Solve the equation: $$-2x^2 + 4x = 9$$

Rearranging gives $$-2x^2 + 4x - 9 = 0$$ . Using the quadratic formula, the solutions are $$x = \frac{{-4 \\pm \text{sqrt}(16 - 72)}}{{-4}} = \frac{{2 \\pm i\text{sqrt}(14)}}{{2}}$$ .

What are complex solutions in the context of quadratic equations?

Complex solutions occur when the discriminant of a quadratic equation is negative, resulting in solutions that include imaginary numbers, expressed in the form $$a + bi$$ .

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

The leading coefficient (the coefficient of $$x^2$$ ) determines the direction of the parabola: if it is positive, the parabola opens upwards; if negative, it opens downwards.

How do you determine the vertex of a parabola represented by a quadratic equation?

The vertex of a parabola given by $$y = ax^2 + bx + c$$ can be found using the formula $$x = -\frac{b}{2a}$$ . The y-coordinate can be found by substituting this x-value back into the equation.

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. It can be found using the formula $$x = -\frac{b}{2a}$$ .

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants and @@a eq 0@@.

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.

How can you convert from standard form to vertex form?

To convert from standard form $$y = ax^2 + bx + c$$ to vertex form, complete the square on the quadratic expression.

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

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

Quadratic Formula/Complex Solutions: Drummond's version Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

2.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

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

15 questions

Anatomy Review

Flashcard

•

12th Grade

9 questions

Inequalities

Flashcard

•

9th Grade

11 questions

Climate Change and Its Causes

Flashcard

•

KG

15 questions

Sleep and Dreams - AP Psychology

Flashcard

•

12th Grade - University

10 questions

Essential Statistics Concepts

Flashcard

•

12th Grade

10 questions

R2.3 How Far? Le Chatelier's Principle

Flashcard

•

12th Grade

10 questions

High Note 2. Unit 1. Test your vocabulary

Flashcard

•

10th Grade

Popular Resources on Wayground

8 questions

2 Step Word Problems

Quiz

•

KG - University

20 questions

Comparing Fractions

Quiz

•

4th Grade

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

10 questions

Latin Bases claus(clois,clos, clud, clus) and ped

Quiz

•

6th - 8th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

7 questions

The Story of Books

Quiz

•

6th - 8th Grade

Discover more resources for Mathematics

8 questions

2 Step Word Problems

Quiz

•

KG - University

13 questions

Model Exponential Growth and Decay Scenarios

Quiz

•

9th - 12th Grade

15 questions

TSI Math Practice Questions

Quiz

•

8th - 12th Grade

24 questions

Identify Properties of Polygons and Quadrilaterals

Quiz

•

9th - 12th Grade

25 questions

Simplify Expressions with Exponents

Quiz

•

9th - 12th Grade

20 questions

Basic Trig Ratios

Quiz

•

9th - 12th Grade

15 questions

Exponential Growth and Decay Word Problems

Quiz

•

9th - 12th Grade

16 questions

Identify and Analyze Geometric Sequences

Quiz

•

9th - 12th Grade