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Solving Quadratic Equations: Easy Steps and Fun Worksheets

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Solving Quadratic Equations: Easy Steps and Fun Worksheets
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Maria Hernandez

@mariahernandez

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117 Followers

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The quadratic formula provides an efficient method for solving quadratic equations. This summary explores its application and various examples.

Quadratic Formula: For ax² + bx + c = 0, x = (-b ± √(b² - 4ac)) / (2a)

Key points:

  • Used when factoring is difficult or impossible
  • Requires identifying coefficients a, b, and c
  • Can solve equations with real or complex roots
  • Useful for finding exact solutions

Examples demonstrate applying the formula to different quadratic equations, including those requiring simplification before solving.

6/30/2023

295

J
The Quadratic formula
Another way to solve quadratic equations is by the quadratic formula.
If ax² + bx+c =0 then x = -b = √b² - 4ac i
2a

The Quadratic Formula

The quadratic formula offers a powerful method for solving quadratic equations when other techniques like factoring prove challenging. This page introduces the formula and provides several examples of its application.

Definition: The quadratic formula states that for a quadratic equation in the form ax² + bx + c = 0, the solutions are given by x = (-b ± √(b² - 4ac)) / (2a).

Highlight: The quadratic formula works for all quadratic equations, even those with complex roots.

The page walks through multiple examples, demonstrating how to:

  1. Identify the coefficients a, b, and c in the equation
  2. Substitute these values into the quadratic formula
  3. Simplify and solve for x

Example: For x² + 8x = -15, the page shows how to rearrange it to standard form (x² + 8x + 15 = 0), identify a=1, b=8, c=15, and then apply the formula to find solutions x = -5 and x = -3.

Additional examples include:

  • Solving (2x+7)² = 25 by first simplifying to standard form
  • Writing a quadratic equation given its roots (-2 and -3)
  • Solving x² + 5x - 10 = 0, demonstrating a case where the solution involves a square root that cannot be simplified further

Vocabulary: Standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

The page concludes with a complex example: (2x+3)(x+4) = 1, showing how to expand and rearrange before applying the quadratic formula.

This comprehensive guide provides students with the tools to solve quadratic equations using the quadratic formula across a variety of problem types, reinforcing the formula's versatility and importance in algebra.

Can't find what you're looking for? Explore other subjects.

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Knowunity is the # 1 ranked education app in five European countries

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iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Solving Quadratic Equations: Easy Steps and Fun Worksheets

user profile picture

Maria Hernandez

@mariahernandez

·

117 Followers

Follow

The quadratic formula provides an efficient method for solving quadratic equations. This summary explores its application and various examples.

Quadratic Formula: For ax² + bx + c = 0, x = (-b ± √(b² - 4ac)) / (2a)

Key points:

  • Used when factoring is difficult or impossible
  • Requires identifying coefficients a, b, and c
  • Can solve equations with real or complex roots
  • Useful for finding exact solutions

Examples demonstrate applying the formula to different quadratic equations, including those requiring simplification before solving.

6/30/2023

295

 

11th/12th

 

Algebra 2

22

J
The Quadratic formula
Another way to solve quadratic equations is by the quadratic formula.
If ax² + bx+c =0 then x = -b = √b² - 4ac i
2a

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The Quadratic Formula

The quadratic formula offers a powerful method for solving quadratic equations when other techniques like factoring prove challenging. This page introduces the formula and provides several examples of its application.

Definition: The quadratic formula states that for a quadratic equation in the form ax² + bx + c = 0, the solutions are given by x = (-b ± √(b² - 4ac)) / (2a).

Highlight: The quadratic formula works for all quadratic equations, even those with complex roots.

The page walks through multiple examples, demonstrating how to:

  1. Identify the coefficients a, b, and c in the equation
  2. Substitute these values into the quadratic formula
  3. Simplify and solve for x

Example: For x² + 8x = -15, the page shows how to rearrange it to standard form (x² + 8x + 15 = 0), identify a=1, b=8, c=15, and then apply the formula to find solutions x = -5 and x = -3.

Additional examples include:

  • Solving (2x+7)² = 25 by first simplifying to standard form
  • Writing a quadratic equation given its roots (-2 and -3)
  • Solving x² + 5x - 10 = 0, demonstrating a case where the solution involves a square root that cannot be simplified further

Vocabulary: Standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

The page concludes with a complex example: (2x+3)(x+4) = 1, showing how to expand and rearrange before applying the quadratic formula.

This comprehensive guide provides students with the tools to solve quadratic equations using the quadratic formula across a variety of problem types, reinforcing the formula's versatility and importance in algebra.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying