1. Equations & Inequalities

The Quadratic Formula

1. Equations & Inequalities

# The Quadratic Formula - Video Tutorials & Practice Problems

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concept

## Solving Quadratic Equations Using The Quadratic Formula

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2

Problem

ProblemSolve the given quadratic equation using the quadratic formula. $3x^2+4x+1=0$

A

$x=3,x=-1$

B

$x=-\frac13,x=-1$

C

$x=-3,x=-1$

D

$x=\frac13,x=-1$

3

Problem

ProblemSolve the given quadratic equation using the quadratic formula. $2x^2-3x=-3$

A

$x=\frac34+\frac{i\sqrt{15}}{4},x=\frac34-\frac{i\sqrt{15}}{4}$

B

$x=\frac34+\frac{5i}{4},x=\frac34-\frac{5i}{4}$

C

$x=\frac{3+\sqrt{15}}{4},x=\frac{3-\sqrt{15}}{4}$

D

$x=3+i\sqrt{15},x=3-i\sqrt{15}$

4

concept

## The Discriminant

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4mPlay a video:

5

Problem

ProblemDetermine the number and type of solutions of the given quadratic equation. Do not solve.

$x^2+8x+16=0$

A

2 real solutions

B

1 real solution

C

2 imaginary solutions

6

Problem

ProblemDetermine the number and type of solutions of the given quadratic equation. Do not solve.

$-4x^2+4x+5=0$

A

2 real solutions

B

1 real solution

C

2 imaginary solutions

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PRACTICE PROBLEMS AND ACTIVITIES (60)

- Match the equation in Column I with its solution(s) in Column II. x^2 = 25
- Match the equation in Column I with its solution(s) in Column II. x^2 = -25
- Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x...
- Answer each question. Answer each question. Unknown NumbersUse the following facts.If x represents an integer,...
- Solve each equation in Exercises 1 - 14 by factoring. 2x(x - 3) = 5x^2 - 7x
- Solve each equation using the zero-factor property. See Example 1. x^2 - 5x + 6 = 0
- Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)
- Solve each equation in Exercises 1 - 14 by factoring. 10x - 1 = (2x + 1)^2
- Answer each question. Answer each question. Answer each question. Unknown NumbersUse the following facts.If x ...
- Answer each question. Answer each question. Answer each question. Unknown NumbersUse the following facts.If x ...
- Solve each equation in Exercises 15–34 by the square root property. (x + 2)^2 = 25
- Solve each problem. See Examples 1. Dimensions of a Parking Lot. A parking lot has a rectangular area of 40,00...
- Solve each equation in Exercises 15–34 by the square root property. 3(x - 4)^2 = 15
- Solve each equation in Exercises 15–34 by the square root property. (x + 3)^2 = - 16
- Solve each equation using the square root property. See Example 2. x^2 = 121
- Solve each equation using the square root property. See Example 2. x^2 = -400
- Solve each equation using the square root property. See Example 2. (x - 4)^2 = -5
- Solve each equation in Exercises 15–34 by the square root property. (2x + 8)^2 = 27
- In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect s...
- Solve each equation. -2x² +11x = -21
- Solve each equation. (2x+1)(x-4) = x
- (Modeling)Solve each problem. See Example 3.Height of a ProjectileA projectile is launched from ground level w...
- Solve each equation using completing the square. See Examples 3 and 4. 2x^2 + x = 10
- Solve each equation using completing the square. See Examples 3 and 4. 3x^2 + 2x = 5
- Solve each equation in Exercises 47–64 by completing the square. x^2 + 6x = 7
- See Exercise 47. (b)Which equation has two nonreal complex solutions?
- Solve each equation in Exercises 47–64 by completing the square. x^2 - 2x = 2
- Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. 8x² = ...
- Solve each equation in Exercises 47–64 by completing the square. x^2 - 6x - 11 = 0
- Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 = 2x - 5
- Solve each equation using the quadratic formula. See Examples 5 and 6. -4x^2 = -12x + 11
- Solve each equation in Exercises 47–64 by completing the square. 2x^2 - 7x + 3 = 0
- Solve each equation in Exercises 47–64 by completing the square. 4x^2 - 4x - 1 = 0
- Solve each equation in Exercises 60–63 by the square root property. x^2/2 + 5 = -3
- Solve each equation in Exercises 47–64 by completing the square. 3x^2 - 5x - 10 = 0
- In Exercises 64–65, determine the constant that should be added to the binomial so that it becomes a perfect s...
- Solve each equation in Exercises 66–67 by completing the square. 3x^2 -12x+11= 0
- Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. s = (1/2)gt^2, ...
- Solve each equation in Exercises 65–74 using the quadratic formula. 4x^2 = 2x + 7
- Solve each equation in Exercises 65–74 using the quadratic formula. x^2 - 6x + 10 = 0
- Exercises 73–75 will help you prepare for the material covered in the next section. Multiply: (7 - 3x)(- 2 - ...
- In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given eq...
- In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given eq...
- For each equation, (b) solve for y in terms of x. See Example 8. 2x^2 + 4xy - 3y^2 = 2
- Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and te...
- Solve each equation in Exercises 83–108 by the method of your choice. 5x^2 + 2 = 11x
- Solve each equation in Exercises 83–108 by the method of your choice. 3x^2 = 60
- Answer each question. Find the values of a, b, and c for which the quadratic equation. ax^2 + bx + c = 0 has ...
- Answer each question. Find the values of a, b, and c for which the quadratic equation. ax^2 + bx + c = 0 has ...
- Solve each equation in Exercises 83–108 by the method of your choice. 9 - 6x + x^2 = 0
- Solve each equation in Exercises 83–108 by the method of your choice. 4x^2 - 16 = 0
- Solve each equation in Exercises 83–108 by the method of your choice. x^2 - 4x + 29 = 0
- Exercises 100–102 will help you prepare for the material covered in the next section. Factor: x^2 - 6x + 9
- Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 3) = 1/4
- Solve each equation in Exercises 83–108 by the method of your choice. 2x/(x - 3) + 6/(x + 3) = - 28/(x^2 - 9)
- Solve each equation in Exercises 83–108 by the method of your choice. 3/(x - 3) + 5/(x - 4) = (x^2 - 20)/(x^2...
- In Exercises 115–122, find all values of x satisfying the given conditions. y1 = x - 1, y2 = x + 4 and y1y2 =...
- In Exercises 115–122, find all values of x satisfying the given conditions. y1 = 2x^2 + 5x - 4, y2 = - x^2 + ...
- In Exercises 127–130, solve each equation by the method of your choice. 1/(x^2 - 3x + 2) = 1/(x + 2) + 5/(x^2...
- Write a quadratic equation in general form whose solution set is {- 3, 5}.