Algebra 2 4-2 Guided Practice: Standard Form of a Quadratic Function

By Matt Richardson

Last updated over 1 year ago

14 Questions

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

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

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.

Graph the function at desmos.com/calculator and use your graph to respond to the Solve It! item below.

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

 0.202 ft

0.2475 ft

0.45 ft

0.175 ft

F.IF.4

A.CED.2

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

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Write the standard form of a quadratic function. Assume a ≠ 0 and use function notation beginning with "f(x)=". 
HINT: Your equation should include a, b, and c.

Take Note: Some information about the quadratic function, including the location of the vertex, is "hidden" when the function is written in standard form. That seems like a disadvantage of the form. Identify and describe one advantage of standard form that was named in this lesson?

Problem 1 Got It?

A

B

C

F.IF.4

A.CED.2

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

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Consider the standard form of a quadratic function.
You can derive a lot of information about the graph of a quadratic function from its coefficients when written in standard form. 

Match items on the left with those on the right to complete true statements about the graphs of quadratics that are written in standard form.

		(0, c).
		the axis of symmetry.
		f\left(x\right)=ax^{2}+bx+c,\ \ \ a\ne 0.
		the parabola opens upward.
		the parabola opens downward.
		the x-coordinate of the vertex.
		the y-coordinate of the vertex.

Problem 2 Got It? What is the graph of the function? 

Plot the vertex, followed by the y-intercept to create the graph.

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.
After you have plotted all graphs, click on x or y intercept tab to graph the intercepts.

Graph 1

y-intercept

10.

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

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

11.

Problem 3 Got It?

A

B

C

D

F.IF.9

A.CED.2

12.

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

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

13.

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 graph the function at desmos.com/calculator and use your graph to help you respond.

72 ft

6 ft

183 ft

4 ft

F.IF.4

A.CED.2

14.

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