1. Equations & Inequalities

Intro to Quadratic Equations

1. Equations & Inequalities

# Intro to Quadratic Equations - Video Tutorials & Practice Problems

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## Introduction to Quadratic Equations

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2

Problem

ProblemWrite the given quadratic equation in standard form. Identify a, b, and c. $-4x^2+x=8$

A

a = - 4, b = 0, c = - 8

B

a = - 4, b = 1, c = 8

C

a = - 4, b = 1, c = - 8

D

a = 2, b = 1, c = 0

3

concept

## Solving Quadratic Equations by Factoring

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4

Problem

ProblemSolve the given quadratic equation by factoring. $3x^2+12x=0$

A

$x=3,x=4$

B

$x=0,x=-4$

C

$x=-3,x=-4$

D

$x=1,x=4$

5

Problem

ProblemSolve the given equation by factoring. $2x^2+7x+6=0$

A

$x=3,x=\frac67$

B

$x=-2,x=0$

C

$x=2,x=\frac32$

D

$x=-2,x=-\frac32$

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PRACTICE PROBLEMS AND ACTIVITIES (97)

- Match the equation in Column I with its solution(s) in Column II. x^2 = 25
- Solve each equation in Exercises 1 - 14 by factoring. x^2 = 8x - 15
- Match the equation in Column I with its solution(s) in Column II. x^2 - 5 = 0
- Solve each equation in Exercises 1 - 14 by factoring. 6x^2 + 11x - 10 = 0
- Solve each equation in Exercises 1 - 14 by factoring. 3x^2 - 2x = 8
- Solve each equation in Exercises 1 - 14 by factoring. 3x^2 + 12x = 0
- 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,...
- Answer each question. Answer each question. Answer each question. Unknown NumbersUse the following facts.If x ...
- 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...
- 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. Answer each question. Unknown NumbersUse the following facts.If x ...
- Solve each equation in Exercises 15–34 by the square root property. 3x^2 = 27
- 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. 5x^2 = 45
- Solve each equation using the zero-factor property. See Example 1. 2x^2 - x = 15
- Solve each equation using the zero-factor property. See Example 1. -6x^2 + 7x = -10
- Solve each equation in Exercises 15–34 by the square root property. 3x^2 - 1 = 47
- Solve each equation in Exercises 15–34 by the square root property. 2x^2 - 5 = - 55
- Solve each problem. See Examples 1 and 2. Dimensions of a Square. The length of each side of a square is 3 in....
- Solve each equation using the zero-factor property. See Example 1. 9x^2 - 12x + 4 = 0
- Solve each problem. See Examples 1. Dimensions of a Parking Lot. A parking lot has a rectangular area of 40,00...
- Solve each equation using the zero-factor property. See Example 1. 36x^2 + 60x + 25 = 0
- Solve each equation in Exercises 15–34 by the square root property. (x - 3)^2 = - 5
- Solve each equation using the square root property. See Example 2. 48 - x^2 = 0
- Solve each equation in Exercises 15–34 by the square root property. (3x + 2)^2 = 9
- Manufacturing to Specifications. A manufacturing firm wants to package its product in a cylindrical container ...
- Solve each equation using the square root property. See Example 2. x^2 = -400
- Solve each equation in Exercises 15–34 by the square root property. (4x - 1)^2 = 16
- Solve each equation in Exercises 15–34 by the square root property. (8x - 3)^2 = 5
- Radius of a CanA can of Blue Runner Red Kidney Beans has surface area 371 cm^2. Its height is 12 cm. What is t...
- Solve each equation using completing the square. See Examples 3 and 4. x^2 - 7x + 12 = 0
- In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect s...
- Solve each problem. See Example 2. Length of a WalkwayA nature conservancy group decides to construct a raised...
- In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect s...
- Solve each equation using completing the square. See Examples 3 and 4. x^2 - 2x - 2 = 0
- Solve each equation. -2x² +11x = -21
- Solve each equation using completing the square. See Examples 3 and 4. 2x^2 + x = 10
- Solve each equation. (2x+1)(x-4) = x
- In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect s...
- Solve each equation using completing the square. See Examples 3 and 4. -3x^2 + 6x + 5 = 0
- Solve each equation. (x+4)(x+2) = 2x
- Which equation has two real, distinct solutions? Do not actually solve. A. (3x-4)² = -9 B. (4-7x)² = 0 C. (5x-...
- Solve each equation using completing the square. See Examples 3 and 4. 3x^2 - 9x + 7 = 0
- Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - x - 1 = 0
- Solve each equation in Exercises 47–64 by completing the square. x^2 - 6x - 11 = 0
- Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. 16x² +...
- Solve each equation in Exercises 47–64 by completing the square. x^2 + 4x + 1 = 0
- Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - 6x = -7
- Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 = 2x - 5
- Solve each equation in Exercises 47–64 by completing the square. x^2 - 5x + 6 = 0
- Solve each equation in Exercises 47–64 by completing the square. x^2 + 3x - 1 = 0
- Solve each equation in Exercises 58–59 by factoring. 2x^2 +15x = 8
- Solve each problem. Dimensions of a Right TriangleThe shortest side of a right triangle is 7 in. shorter than ...
- Solve each equation using the quadratic formula. See Examples 5 and 6. 2/3x^2 + 1/4x = 3
- Solve each equation using the quadratic formula. See Examples 5 and 6. (4x - 1)(x + 2) = 4x
- Solve each equation in Exercises 47–64 by completing the square. 3x^2 - 5x - 10 = 0
- Solve each equation in Exercises 65–74 using the quadratic formula. x^2 + 8x + 15 = 0
- Solve each equation in Exercises 65–74 using the quadratic formula. x^2 + 5x + 3 = 0
- Solve each cubic equation using factoring and the quadratic formula. See Example 7. x^3 - 27 = 0
- Solve each equation in Exercises 65–74 using the quadratic formula. 3x^2 - 3x - 4 = 0
- Solve each cubic equation using factoring and the quadratic formula. See Example 7. x^3 + 64 = 0
- Solve each equation in Exercises 68–70 using the quadratic formula. 2x^2 = 3-4x
- In Exercises 71–72, without solving the given quadratic equation, determine the number and type of solutions. ...
- Solve each equation in Exercises 73–81 by the method of your choice. 3x^2-7x+1 =0
- Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. r = r_0+(1/2)at...
- Solve each equation in Exercises 73–81 by the method of your choice. (x-3)^2 - 25 = 0
- Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. h = -16t^2+v_0t...
- 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. 4x^2 - 2xy + 3y^2 = 2
- For each equation, (a) solve for x in terms of y. See Example 8. 2x^2 + 4xy - 3y^2 = 2
- In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given eq...
- Solve each equation in Exercises 83–108 by the method of your choice. 2x^2 - x = 1
- Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and te...
- Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and te...
- 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. (2x + 3)(x + 4) = 1
- Solve each equation in Exercises 83–108 by the method of your choice. (2x - 5)(x + 1) = 2
- Solve each equation in Exercises 83–108 by the method of your choice. (3x - 4)^2 = 16
- 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. 3x^2 - 12x + 12 = 0
- Solve by completing the square: 2x² – 5x + 1 = 0.
- Solve each equation in Exercises 83–108 by the method of your choice. x^2 - 4x + 29 = 0
- Solve each equation in Exercises 83–108 by the method of your choice. x^2 = 4x - 7
- Solve each equation in Exercises 83–108 by the method of your choice. 2x^2 - 7x = 0
- Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 2) = 1/3
- In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the...
- In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the...
- In Exercises 115–122, find all values of x satisfying the given conditions. y = 2x^2 - 3x and y = 2
- In Exercises 115–122, find all values of x satisfying the given conditions. y = 5x^2 + 3x and y = 2
- In Exercises 115–122, find all values of x satisfying the given conditions. y1 = 2x^2 + 5x - 4, y2 = - x^2 + ...
- In Exercises 115–122, find all values of x satisfying the given conditions. y1 = - x^2 + 4x - 2, y2 = - 3x^2 ...
- When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the...
- When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Fi...
- Write a quadratic equation in general form whose solution set is {- 3, 5}.