Algebra 2 4-1 Guided Practice: Quadratic Functions and Transformations

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! In the computer game Steeplechase, you press the "jump" button and the horse makes the jump shown. The highest part of the jump must be directly above the fence or you lose time.

Solve It! Where should this horse be when you press "jump"?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: The sketch of a graph may omit most graph details. Sketches may be created more quickly than standard graphs and with less precision.

Take Note: Define parabola. Also, sketch a parabola on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: Define quadratic function.

Take Note: The standard form of a quadratic function is as follows:
f(x)=ax^{2}+bx+c
(Note that a ≠ 0)

One strategy to associate this form with the name standard is to consider the a-b-c pattern it contains.

Another form, vertex form, is so named because it reveals the vertex of the parabola it creates when graphed.

Write the general vertex form of a quadratic function in the response field (assume that a ≠ 0).

HINT: Your equation should include f(x), a, x, h, and k.

Take Note: Define axis of symmetry of a parabola. Also, sketch and label the axis of symmetry of the parabola on the canvas using a contrasting color.

Take Note: Define vertex of a parabola. Also, label the vertex of the parabola on the canvas using a contrasting color.

Take Note: Write the parent quadratic function in the response field. Also, sketch the parent quadratic function on the canvas using a contrasting color.

Problem 1 Got It? What is the graph of the function? Complete a table of values and graph the function on the canvas. Use colors other than black.

Hint: consider choosing values of x for your table that cancel out the fraction when multiplied. x = 0, 3, and -3 work well.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 1 Got It? Graph the parent quadratic function and its transformation on the same plane. Zoom and pan your graph to establish an appropriate viewing window. Consider the relationship between the two functions.
Graph 1: y_1=x^{2}
Graph 2: y_2=-\frac{1}{3}x^2

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

Problem 1 Got It? Reasoning: What can you say about the graph of the function below if a is a negative number?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Consider transformations of graph of the parent quadratic function of the form f(x)=ax^2.
Match each item on the left with the type of transformation it represents.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

f(x)=ax^{2}, 0<a<1
f(x)=ax^{2}, a>1
f(x)=-ax^2 (a becomes -a)

Reflection (across the horizontal axis)
Stretch (vertical)
Compression (vertical)

Take Note: Define minimum value (of a parabola). Be sure to indicate whether the x-coordinate or the y-coordinate represents the minimum value.

Take Note: Define maximum value (of a parabola). Be sure to indicate whether the x-coordinate or the y-coordinate represents the maximum value.

Take Note: Describe why it is not possible for a parabola to have both a maximum value and a minimum value.

Problem 2 Got It? Graph the function on the canvas. Complete this item without Desmos or a graphing calculator. Consider that it is simply a translation of the parent function. You may then check your work at Desmos.

Include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior as appropriate.

Problem 2 Got It? How is the graph of g(x) = x² + 3 in the previous item a translation of the graph of the parent function f(x) = x² ?

Problem 2 Got It? Graph the function on the canvas. Complete this item without Desmos or a graphing calculator. Consider that it is simply a translation of the parent function. You may then check your work at Desmos.

Include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior as appropriate.

Problem 2 Got It? How is the graph of h(x) = (x + 1)² in the previous item a translation of the graph of the parent function f(x) = x² ?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Assume that you are given a quadratic function written in vertex form.
Describe the following
1) The process for finding the vertex of the associated parabola
2) The process for determining whether the associated parabola opens upward or opens downward
3) The process for determining if k represents the minimum or maximum value of the function

Problem 3 Got It?

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Problem 4 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 5 Got It? Suppose the path of the jump changes so that the axis of symmetry becomes x = 2 and the height stays the same, 7. If the path of the jump also passes through the point (5, 5), what quaratic function would model this path?

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🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! Where should this horse be when you press "jump"?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define parabola. Also, sketch a parabola on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: Define quadratic function.

Take Note: Define axis of symmetry of a parabola. Also, sketch and label the axis of symmetry of the parabola on the canvas using a contrasting color.

Take Note: Define vertex of a parabola. Also, label the vertex of the parabola on the canvas using a contrasting color.

Take Note: Write the parent quadratic function in the response field. Also, sketch the parent quadratic function on the canvas using a contrasting color.

Problem 1 Got It? Graph the parent quadratic function and its transformation on the same plane. Zoom and pan your graph to establish an appropriate viewing window. Consider the relationship between the two functions.
Graph 1: y_1=x^{2}
Graph 2: y_2=-\frac{1}{3}x^2

Problem 1 Got It? Reasoning: What can you say about the graph of the function below if a is a negative number?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define minimum value (of a parabola). Be sure to indicate whether the x-coordinate or the y-coordinate represents the minimum value.

Take Note: Define maximum value (of a parabola). Be sure to indicate whether the x-coordinate or the y-coordinate represents the maximum value.

Take Note: Describe why it is not possible for a parabola to have both a maximum value and a minimum value.

Problem 2 Got It? How is the graph of g(x) = x² + 3 in the previous item a translation of the graph of the parent function f(x) = x² ?

Problem 2 Got It? How is the graph of h(x) = (x + 1)² in the previous item a translation of the graph of the parent function f(x) = x² ?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 3 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Consider transformations of the graph of a quadratic function written in vertex form.
What impact does the value of a have on the graph? Select all that apply.

Take Note: Consider transformations of the graph of a quadratic function written in vertex form.
What impact does the value of h have on the graph? Select all that apply.

Take Note: Consider transformations of the graph of a quadratic function written in vertex form.
What impact does the value of k have on the graph? Select all that apply.

Take Note: Sketch a horizontal translation of the parabola on the canvas. Use a contrasting color.

Take Note: Sketch a vertical translation of the parabola on the canvas. Use a contrasting color.

Problem 4 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 5 Got It? Suppose the path of the jump changes so that the axis of symmetry becomes x = 2 and the height stays the same, 7. If the path of the jump also passes through the point (5, 5), what quaratic function would model this path?

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Algebra 2 4-1 Guided Practice: Quadratic Functions and Transformations

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! Where should this horse be when you press "jump"?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define parabola. Also, sketch a parabola on the canvas.You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: Define quadratic function.

Take Note: Define axis of symmetry of a parabola. Also, sketch and label the axis of symmetry of the parabola on the canvas using a contrasting color.

Take Note: Define vertex of a parabola. Also, label the vertex of the parabola on the canvas using a contrasting color.

Take Note: Write the parent quadratic function in the response field. Also, sketch the parent quadratic function on the canvas using a contrasting color.

Problem 1 Got It? Graph the parent quadratic function and its transformation on the same plane. Zoom and pan your graph to establish an appropriate viewing window. Consider the relationship between the two functions.Graph 1: y_1=x^{2}Graph 2: y_2=-\frac{1}{3}x^2

Problem 1 Got It? Reasoning: What can you say about the graph of the function below if a is a negative number?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define minimum value (of a parabola). Be sure to indicate whether the x-coordinate or the y-coordinate represents the minimum value.

Take Note: Define maximum value (of a parabola). Be sure to indicate whether the x-coordinate or the y-coordinate represents the maximum value.

Take Note: Describe why it is not possible for a parabola to have both a maximum value and a minimum value.

Problem 2 Got It? How is the graph of g(x) = x² + 3 in the previous item a translation of the graph of the parent function f(x) = x² ?

Problem 2 Got It? How is the graph of h(x) = (x + 1)² in the previous item a translation of the graph of the parent function f(x) = x² ?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 3 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Consider transformations of the graph of a quadratic function written in vertex form. What impact does the value of a have on the graph? Select all that apply.

Take Note: Consider transformations of the graph of a quadratic function written in vertex form. What impact does the value of h have on the graph? Select all that apply.

Take Note: Consider transformations of the graph of a quadratic function written in vertex form. What impact does the value of k have on the graph? Select all that apply.

Take Note: Sketch a horizontal translation of the parabola on the canvas. Use a contrasting color.

Take Note: Sketch a vertical translation of the parabola on the canvas. Use a contrasting color.

Problem 4 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 5 Got It? Suppose the path of the jump changes so that the axis of symmetry becomes x = 2 and the height stays the same, 7. If the path of the jump also passes through the point (5, 5), what quaratic function would model this path?

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Define parabola. Also, sketch a parabola on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 1 Got It? Graph the parent quadratic function and its transformation on the same plane. Zoom and pan your graph to establish an appropriate viewing window. Consider the relationship between the two functions.
Graph 1: y_1=x^{2}
Graph 2: y_2=-\frac{1}{3}x^2

Take Note: Consider transformations of the graph of a quadratic function written in vertex form.
What impact does the value of a have on the graph? Select all that apply.

Take Note: Consider transformations of the graph of a quadratic function written in vertex form.
What impact does the value of h have on the graph? Select all that apply.

Take Note: Consider transformations of the graph of a quadratic function written in vertex form.
What impact does the value of k have on the graph? Select all that apply.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?