Algebra 2 4-2 Complete Lesson: Standard Form of a Quadratic Function

Solve It! The function below models the height h of a soccer ball as it travels distance x. 

NOTE: This is not the ball in the image.

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We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

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Problem 1 Got It?

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Problem 2 Got It? What is the graph of the function? Use the vertex, y-intercept, and axis of symmetry to sketch the graph. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

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Problem 3 Got It?

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Problem 4 Got It? The Zhaoshou Bridge in China is the oldest known arch bridge, dating to AD 605.

You can model the support arch with the function below where x and f are measured in feet. Graph the function. Zoom and pan your graph to establish an appropriate viewing window. Keep in mind that negative values for x and y are not applicable.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

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Problem 4 Got It? The Zhaoshou Bridge in China is the oldest known arch bridge, dating to AD 605.

You can model the support arch with the function below where x and f are measured in feet. How high is the arch above its supports? You may refer to your graph in the previous item.

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Vocabulary: Does the parbola have a maximum?

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Graphing: Graph the function. Sketch the function yourself before using a graphing utility, like the embedded Desmos graphing calculator, to check your work. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

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Graphing: Graph the function. Sketch the function yourself before using a graphing utility, like the embedded Desmos graphing calculator, to check your work. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

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Error Analysis: A student graphed the function below as shown in the image.
Find and correct the error.

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Review Lesson 1-4: Solve the equation. Enter only a number in decimal form.

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Review Lesson 3-2: Classify each system to indicate which is better-suited to solving by substitution and which is better-suited to solving by elimination.

One system should be classified as substitution and one should be classified as elimination.

Substitution
Elimination

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Review Lesson 4-2: Identify the vertex, axis of symmetry, the maximum or minimum value, and the domain and range of the function. Use each draggable value once.

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Vocabulary Review: Drag the tags to label the functions based on whether or not they are in standard form.

standard form
NOT standard form

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Use Your Vocabulary: Identify the graph(s) of quadratic functions.

Quadratic function(s)

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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

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Algebra 2 4-2 Complete Lesson: Standard Form of a Quadratic Function

Problem 1 Got It?

Problem 2 Got It? What is the graph of the function? Use the vertex, y-intercept, and axis of symmetry to sketch the graph. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Problem 3 Got It?

Problem 4 Got It? The Zhaoshou Bridge in China is the oldest known arch bridge, dating to AD 605.

You can model the support arch with the function below where x and f are measured in feet. How high is the arch above its supports? You may refer to your graph in the previous item.

Vocabulary: Does the parbola have a maximum?

Error Analysis: A student graphed the function below as shown in the image.
Find and correct the error.

Review Lesson 1-4: Solve the equation. Enter only a number in decimal form.

Review Lesson 3-2: Classify each system to indicate which is better-suited to solving by substitution and which is better-suited to solving by elimination.

One system should be classified as substitution and one should be classified as elimination.

Review Lesson 4-2: Identify the vertex, axis of symmetry, the maximum or minimum value, and the domain and range of the function. Use each draggable value once.

Vocabulary Review: Drag the tags to label the functions based on whether or not they are in standard form.

Use Your Vocabulary: Identify the graph(s) of quadratic functions.

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! Graph the parabola representing the path of the ball. Zoom and pan your graph to establish an appropriate viewing window.

Solve It! What is the maximum height of the ball?

Problem 1 Got It?

Problem 2 Got It? What is the graph of the function? Use the vertex, y-intercept, and axis of symmetry to sketch the graph. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Problem 3 Got It?

Problem 4 Got It? The Zhaoshou Bridge in China is the oldest known arch bridge, dating to AD 605.

You can model the support arch with the function below where x and f are measured in feet. How high is the arch above its supports? You may refer to your graph in the previous item.

Vocabulary: Identify the vertex of the parabola.

Vocabulary: Identify the axis of symetry of the parabola.

Vocabulary: Identify the minimum of the parabola.

Vocabulary: Does the parbola have a maximum?

Error Analysis: A student graphed the function below as shown in the image.
Find and correct the error.

Review Lesson 1-4: Solve the equation. Enter only a number in decimal form.

Review Lesson 3-2: Classify each system to indicate which is better-suited to solving by substitution and which is better-suited to solving by elimination.

One system should be classified as substitution and one should be classified as elimination.

Review Lesson 4-2: Identify the vertex, axis of symmetry, the maximum or minimum value, and the domain and range of the function. Use each draggable value once.

Vocabulary Review: Drag the tags to label the functions based on whether or not they are in standard form.

Use Your Vocabulary: Identify the graph(s) of quadratic functions.

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! What is the maximum height of the ball?

Vocabulary: Identify the vertex of the parabola.

Vocabulary: Identify the axis of symetry of the parabola.

Vocabulary: Identify the minimum of the parabola.

Algebra 2 4-2 Complete Lesson: Standard Form of a Quadratic Function

Algebra 2 4-2 Complete Lesson: Standard Form of a Quadratic Function

Problem 1 Got It?

Problem 2 Got It? What is the graph of the function? Use the vertex, y-intercept, and axis of symmetry to sketch the graph. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Problem 3 Got It?

Problem 4 Got It? The Zhaoshou Bridge in China is the oldest known arch bridge, dating to AD 605. You can model the support arch with the function below where x and f are measured in feet. How high is the arch above its supports? You may refer to your graph in the previous item.

Vocabulary: Does the parbola have a maximum?

Error Analysis: A student graphed the function below as shown in the image.Find and correct the error.

Review Lesson 1-4: Solve the equation. Enter only a number in decimal form.

Review Lesson 3-2: Classify each system to indicate which is better-suited to solving by substitution and which is better-suited to solving by elimination. One system should be classified as substitution and one should be classified as elimination.

Review Lesson 4-2: Identify the vertex, axis of symmetry, the maximum or minimum value, and the domain and range of the function. Use each draggable value once.

Vocabulary Review: Drag the tags to label the functions based on whether or not they are in standard form.

Use Your Vocabulary: Identify the graph(s) of quadratic functions.

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! Graph the parabola representing the path of the ball. Zoom and pan your graph to establish an appropriate viewing window.

Solve It! What is the maximum height of the ball?

Problem 1 Got It?

Problem 2 Got It? What is the graph of the function? Use the vertex, y-intercept, and axis of symmetry to sketch the graph. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Problem 3 Got It?

Problem 4 Got It? The Zhaoshou Bridge in China is the oldest known arch bridge, dating to AD 605. You can model the support arch with the function below where x and f are measured in feet. How high is the arch above its supports? You may refer to your graph in the previous item.

Vocabulary: Identify the vertex of the parabola.

Vocabulary: Identify the axis of symetry of the parabola.

Vocabulary: Identify the minimum of the parabola.

Vocabulary: Does the parbola have a maximum?

Error Analysis: A student graphed the function below as shown in the image.Find and correct the error.

Review Lesson 1-4: Solve the equation. Enter only a number in decimal form.

Review Lesson 3-2: Classify each system to indicate which is better-suited to solving by substitution and which is better-suited to solving by elimination. One system should be classified as substitution and one should be classified as elimination.

Review Lesson 4-2: Identify the vertex, axis of symmetry, the maximum or minimum value, and the domain and range of the function. Use each draggable value once.

Vocabulary Review: Drag the tags to label the functions based on whether or not they are in standard form.

Use Your Vocabulary: Identify the graph(s) of quadratic functions.

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! What is the maximum height of the ball?

Vocabulary: Identify the vertex of the parabola.

Vocabulary: Identify the axis of symetry of the parabola.

Vocabulary: Identify the minimum of the parabola.

Problem 4 Got It? The Zhaoshou Bridge in China is the oldest known arch bridge, dating to AD 605.

You can model the support arch with the function below where x and f are measured in feet. How high is the arch above its supports? You may refer to your graph in the previous item.

Error Analysis: A student graphed the function below as shown in the image.
Find and correct the error.

Review Lesson 3-2: Classify each system to indicate which is better-suited to solving by substitution and which is better-suited to solving by elimination.

One system should be classified as substitution and one should be classified as elimination.

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.

Problem 4 Got It? The Zhaoshou Bridge in China is the oldest known arch bridge, dating to AD 605.

You can model the support arch with the function below where x and f are measured in feet. How high is the arch above its supports? You may refer to your graph in the previous item.

Error Analysis: A student graphed the function below as shown in the image.
Find and correct the error.

Review Lesson 3-2: Classify each system to indicate which is better-suited to solving by substitution and which is better-suited to solving by elimination.

One system should be classified as substitution and one should be classified as elimination.

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.