a1tD0000003mM1CIAU

Finding the Vertex in Standard Form

  • 9-12 grade

Lesson Description:

Students will find a vertex of a given parabola in standard form in the theme of Star Wars. Once the student provides the vertex, the BB-8 (Sphero robot) will position itself so it can be picked up by the x-fighter. 


 

Standards Covered

CCSS.MATH.CONTENT.HSF.IF.C.7.A

Graph linear and quadratic functions and show intercepts, maxima, and minima.

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP4

Model with mathematics.

CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6

Attend to precision.

image description

Lesson Modules


Teaching Tips:

Show the video to the class. The video is in the class view. Stop the video at 37 seconds. 

Have the students answer the question. Tell them they can only write their answer in one word. Otherwise, the system won't recognize their answers. 

Share the word-cloud with the class to discuss the key information. 

In Star Wars 7 - The Force Awakens, BB-8 boards on X-fighter. 

Watch the video answer the following question below. You don't need to watch the entire video. Stop at 37 seconds. 




How do you think BB-8 and the x-fighter communicate so BB-8 can be picked up without any mistake? Write your answer only in one word. 

 


Teaching Tips:

Have the students play with the interactive tool. For advanced students, they can try to prove {latexinline{h=\frac{b}{-2a} }latexinline}. 

Play with the interactive tool below. 

Use the sliders to change the variables. If you don't see the parabola, click on the grid-in. 

 

 

More to think about!

With your team members, try to prove that the {latexinline{x }latexinline} value of the vertex of a parabola with a standard form of {latexinline{ax^2+bx+c }latexinline} is always {latexinline{\frac{b}{-2a} }latexinline}. 


Hint:

Let {latexinline{f(x)}latexinline} be a quadratic function, {latexinline{ax^2+bx+c}latexinline}. The equavalent form can be written as {latexinline{f(x)=a(x-h)^2+k }latexinline}, where the vertex is {latexinline{(h,k) }latexinline}.

 

{latex{\begin{align}f(x)&=ax^2+bx+c\\& \qqaud\cdot\\& \qqaud\cdot\\& \qqaud\cdot\\& =a(x-h)^2+k\end{align} }latex}

 

Try to figure out how you can transform the equation into standard form to the vertex form in order to prove that the {latexinline{x}latexinline} value of the vertex is {latexinline{\frac{b}{-2a} }latexinline}.


Teaching Tips:

Use the lesson material for this module. You can print out and place them on a flat surface (on the floor or on the table).  

Select a quadratic function from the list and have students find the coordinate of the vertex.

{latex{y=x^2-2x+2,\space (1,3)\\

y=x^2-4x+3,\space (2.1)\\

y=2x^2-8x+7,\space (2.1)\\

y=-x^2-4x-3,\space (-2,1)\\

y=-2x^2-8x-7,\space (-2,-1)\\

y=3x^2-18x+23,\space (3,-4)\\

y=4x^2-24x+36,\space (3,0)\\}latex}

Whichever team answers the first gets to play with the Sphero robot. When they control the Sphero robot, the goal is to make the robot go to the vertex. 

Use this material for the activity. You can print out and place them on a flat surface like a floor or a table.

Find the vertex of the quadratic equations. Check answer and if your answer is correct, place the Sphero robot at any point on the printed material and move the robot to the vertex of a parabola.


{latex{y=x^2-2x+2}latex}

(1, 3)


{latex{y=x^2-4x+3}latex}

(2, 1)


{latex{y=2x^2-8x+7}latex} 

(2, 1)


{latex{y=-x^2-4x-3}latex}

(-2, 1)


{latex{y=-2x^2-8x-7}latex}

(-2, -1)


{latex{y=3x^2-18x+23}latex}

(3, -4)


{latex{y=4x^2-24x+36}latex}

(3, 0)



Teaching Tips:

Give students a quiet time to answer the questions individually. 

Share the bar/pie to the class to review how the class understands the key concepts of this lesson. 

Have a quick discussion on what went well and what could've done differently. Reflect on the next lesson. 

 

You have access to students' response in your dashboard. 

Have a quiet time individually to answer the following questions. Be honest. No one will judge your answers but your responses will be used for better planning of the next lesson. 


The axis of symmetry is the line {latexinline{x=\frac{b}{-2a} }latexinline}.

I understand the concept of line of symmetry of a parabola.
  • Not at all
  • Kind of got it
  • Understand
  • Pretty good
  • Totally got it

Explain how the line of symmetry is related to the vertex.


The x-coordinate of the vertex is {latexinline{\frac{b}{-2a} }latexinline}.

I understand how to find the coordinates of the vertex in a standard form.
  • Not at all
  • Kind of got it
  • Understand
  • Pretty good
  • Totally got it

Explain how to find the coordinate of the vertex in a standard form.