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

Last updated almost 4 years ago
22 questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
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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Solve It! Graph the parabola representing the path of the ball. Zoom and pan your graph to establish an appropriate viewing window.

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

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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.

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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: Identify the vertex of the parabola.

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Vocabulary: Identify the axis of symetry of the parabola.

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Vocabulary: Identify the minimum of the parabola.

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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.

10

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.

  • -1
  • (-2, -1)
  • x = -2
  • all real numbers
  • y ≥ -1
  • Vertex
  • Axis of symmetry
  • Minimum
  • Domain
  • Range
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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)
100

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