Algebra 2 4-7 Complete Lesson: The Quadratic Formula

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Solve It! On this happy face, what quadratic functions have graphs that meet the following conditions? Consider only the domain 2 ≤ x ≤ 6.

◆ crosses the x-axis twice
◆ touches the x-axis only once
◆ misses the x axis completely

crosses the x-axis twice

F.IF.7.a

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Problem 1 Got It?

A.REI.4.b

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Problem 1 Got It?

A.REI.4.b

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A.REI.4.b

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Problem 2 Got It? Reasoning: Would a negative profit make sense in Problem 2? Explain.

A.REI.4.b

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Problem 3 Got It?

A.REI.4.b

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Problem 3 Got It?

A.REI.4.b

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Problem 4 Got It? Reasoning: Will the golf ball in Problem 4 ever reach a height of 110 ft? Use the discriminant to explain your answer.

A.REI.4.b

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A.REI.4.b

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A.REI.4.b

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A.REI.4.b

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A.REI.4.b

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A.REI.4.b

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A.REI.4.b

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A.REI.4.b

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Reasoning: For what value(s) of k does the equation below have one real solution? two real solutions?

k = 6
k > 6
k < 6

The equation has one real solution for the following value(s) of k.
The equation has two real solutions for the following value(s) of k.

A.REI.4.b

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Error Analysis: Your friend concluded that because two discriminants are equal, the solutions to the two equations are the same. Explain your friend's error. Give an example of two quadratic equations that disprove this conclusion.

A.REI.4.b

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Reasoning: If one quadratic equation has a positive discriminant, and another quadratic equation has a discriminant equal to 0, can the two quadratic equations share a solution? Explain why or why not. If so, give two quadratic equations that meet this criterion.

A.REI.4.b

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Review Lesson 4-6: Solve the equation by completing the square. Show your work on the canvas.

A.SSE.3.b

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Review Lesson 1-3: Simplify by combining like terms. Match each expression on the left with its simplified form on the right.

9x² + 4x + 4y
9x² + 3y
4x² - 8x - 2y

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Review Radical Expressions: Match each radical expression on the left with its simplified form on the right.

N.RN.2

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Vocabulary Review: Match each formula with its description.

area of a square
area of a circle

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Use Your Vocabulary: Identify the discriminant of the equation.

A.REI.4.b

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Use Your Vocabulary: Identify the discriminant of the equation.

A.REI.4.b

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Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

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Reflection: Math Success

A.REI.4.b

Algebra 2 4-7 Complete Lesson: The Quadratic Formula

Solve It! On this happy face, what quadratic functions have graphs that meet the following conditions? Consider only the domain 2 ≤ x ≤ 6.

◆ crosses the x-axis twice
◆ touches the x-axis only once
◆ misses the x axis completely

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It? Reasoning: Would a negative profit make sense in Problem 2? Explain.

Problem 3 Got It?

Problem 3 Got It?

Problem 4 Got It? Reasoning: Will the golf ball in Problem 4 ever reach a height of 110 ft? Use the discriminant to explain your answer.

Reasoning: For what value(s) of k does the equation below have one real solution? two real solutions?

Error Analysis: Your friend concluded that because two discriminants are equal, the solutions to the two equations are the same. Explain your friend's error. Give an example of two quadratic equations that disprove this conclusion.

Reasoning: If one quadratic equation has a positive discriminant, and another quadratic equation has a discriminant equal to 0, can the two quadratic equations share a solution? Explain why or why not. If so, give two quadratic equations that meet this criterion.

Review Lesson 4-6: Solve the equation by completing the square. Show your work on the canvas.

Review Lesson 1-3: Simplify by combining like terms. Match each expression on the left with its simplified form on the right.

Review Radical Expressions: Match each radical expression on the left with its simplified form on the right.

Vocabulary Review: Match each formula with its description.

Use Your Vocabulary: Identify the discriminant of the equation.

Use Your Vocabulary: Identify the discriminant of the equation.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! On this happy face, what quadratic functions have graphs that meet the following conditions? Consider only the domain 2 ≤ x ≤ 6.

◆ crosses the x-axis twice
◆ touches the x-axis only once
◆ misses the x axis completely

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It? In Problem 2, what is the least amount you can charge for a CD to make a $100 profit?

Problem 2 Got It? Reasoning: Would a negative profit make sense in Problem 2? Explain.

Problem 3 Got It?

Problem 3 Got It?

Problem 4 Got It? Reasoning: Will the golf ball in Problem 4 ever reach a height of 110 ft? Use the discriminant to explain your answer.

Reasoning: For what value(s) of k does the equation below have one real solution? two real solutions?

Error Analysis: Your friend concluded that because two discriminants are equal, the solutions to the two equations are the same. Explain your friend's error. Give an example of two quadratic equations that disprove this conclusion.

Reasoning: If one quadratic equation has a positive discriminant, and another quadratic equation has a discriminant equal to 0, can the two quadratic equations share a solution? Explain why or why not. If so, give two quadratic equations that meet this criterion.

Review Lesson 4-6: Solve the equation by completing the square. Show your work on the canvas.

Review Lesson 1-3: Simplify by combining like terms. Match each expression on the left with its simplified form on the right.

Review Radical Expressions: Match each radical expression on the left with its simplified form on the right.

Vocabulary Review: Match each formula with its description.

Use Your Vocabulary: Identify the discriminant of the equation.

Use Your Vocabulary: Identify the discriminant of the equation.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Problem 2 Got It? In Problem 2, what is the least amount you can charge for a CD to make a $100 profit?

Algebra 2 4-7 Complete Lesson: The Quadratic Formula

Algebra 2 4-7 Complete Lesson: The Quadratic Formula

Solve It! On this happy face, what quadratic functions have graphs that meet the following conditions? Consider only the domain 2 ≤ x ≤ 6.◆ crosses the x-axis twice◆ touches the x-axis only once◆ misses the x axis completely

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It? Reasoning: Would a negative profit make sense in Problem 2? Explain.

Problem 3 Got It?

Problem 3 Got It?

Problem 4 Got It? Reasoning: Will the golf ball in Problem 4 ever reach a height of 110 ft? Use the discriminant to explain your answer.

Reasoning: For what value(s) of k does the equation below have one real solution? two real solutions?

Error Analysis: Your friend concluded that because two discriminants are equal, the solutions to the two equations are the same. Explain your friend's error. Give an example of two quadratic equations that disprove this conclusion.

Reasoning: If one quadratic equation has a positive discriminant, and another quadratic equation has a discriminant equal to 0, can the two quadratic equations share a solution? Explain why or why not. If so, give two quadratic equations that meet this criterion.

Review Lesson 4-6: Solve the equation by completing the square. Show your work on the canvas.

Review Lesson 1-3: Simplify by combining like terms. Match each expression on the left with its simplified form on the right.

Review Radical Expressions: Match each radical expression on the left with its simplified form on the right.

Vocabulary Review: Match each formula with its description.

Use Your Vocabulary: Identify the discriminant of the equation.

Use Your Vocabulary: Identify the discriminant of the equation.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! On this happy face, what quadratic functions have graphs that meet the following conditions? Consider only the domain 2 ≤ x ≤ 6.◆ crosses the x-axis twice◆ touches the x-axis only once◆ misses the x axis completely

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It? In Problem 2, what is the least amount you can charge for a CD to make a $100 profit?

Problem 2 Got It? Reasoning: Would a negative profit make sense in Problem 2? Explain.

Problem 3 Got It?

Problem 3 Got It?

Problem 4 Got It? Reasoning: Will the golf ball in Problem 4 ever reach a height of 110 ft? Use the discriminant to explain your answer.

Reasoning: For what value(s) of k does the equation below have one real solution? two real solutions?

Error Analysis: Your friend concluded that because two discriminants are equal, the solutions to the two equations are the same. Explain your friend's error. Give an example of two quadratic equations that disprove this conclusion.

Reasoning: If one quadratic equation has a positive discriminant, and another quadratic equation has a discriminant equal to 0, can the two quadratic equations share a solution? Explain why or why not. If so, give two quadratic equations that meet this criterion.

Review Lesson 4-6: Solve the equation by completing the square. Show your work on the canvas.

Review Lesson 1-3: Simplify by combining like terms. Match each expression on the left with its simplified form on the right.

Review Radical Expressions: Match each radical expression on the left with its simplified form on the right.

Vocabulary Review: Match each formula with its description.

Use Your Vocabulary: Identify the discriminant of the equation.

Use Your Vocabulary: Identify the discriminant of the equation.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Problem 2 Got It? In Problem 2, what is the least amount you can charge for a CD to make a $100 profit?

Solve It! On this happy face, what quadratic functions have graphs that meet the following conditions? Consider only the domain 2 ≤ x ≤ 6.

◆ crosses the x-axis twice
◆ touches the x-axis only once
◆ misses the x axis completely

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Solve It! On this happy face, what quadratic functions have graphs that meet the following conditions? Consider only the domain 2 ≤ x ≤ 6.

◆ crosses the x-axis twice
◆ touches the x-axis only once
◆ misses the x axis completely

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.