Lesson: 10-2 Graphing Quadratic Functions

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Lesson Objective

SWBAT graph quadratic functions using a table of values.

Lesson Plan

Teacher: Hall/Lin
Course:    8th Math
Date:     April 8, 2010
 
Objective: 
-          SWBAT  graph quadratic functions
Unit Title:  Quadratics 10
Objective Number: 10-2
 
Materials: do now, cc, packet, textbooks, notebooks, HW, EX, clickers
 
 
Vocabulary: parabola, vertex, axis of symmetry, domain and range
 
 
Do now:
 
Purpose of the do now: 
xCumulative Review _____________
â–¡Activate Prior Knowledge
â–¡Introduce Lesson
â–¡Other ___________________
 
Total Recall / Hook: How will you transition from the Do Now into today’s objective? How will you tie your recall to the importance of today’s objective?
 
Mental math – quadratics review
MENTAL MATH
1- What is the standard form of a linear equation? (ax + by = c) 
2- Name another form of a linear equation.
3- What is the standard form for a quadratic equation?
4- What is the name of the shape of a quadratic graph?
5- Will the graph of y = 1.5x2 open up or open down?
6- What is the GCF of 18x2 and 4x? (2x)
7- How much interest will you earn on a $100 investment at 2% for 1 years? (2 dollars)
8- 2 years? (4 dollars)
9- 5 years? (10 dollars)
10- invest 500 dollars at 5% for 2 years? (50 dollars)
 
Agenda: Outline of your lesson
  1. DN/CC/MM (35)
  2. Lesson (25)
  3. Partners/Guided (15)
  4. IP (30)
5.      Share (5 )
6.      Exit Ticket (5)
 
 
 
 
 
 
Intro to NM
 
Today we are going to learn how to graph quadratics without a graphing calculator. They are not as easy as linear equations, because we can’t just use the slope and intercept. Instead, we have to do it the long way – a table of values.
 
Example 1:
Now you can save your time by being smart about which values you plug in – usually four can be enough to help you sketch the curve. For most graphs, zero is a good place to start.
(Fill in one of the values – be careful when squaring negatives! – have students fill in the rest on their own)
Plot the points – remember, we should see a parabola so if we don’t then we messed up! (usually you can tell which point to fix)
***Notice the symmetry of the graph… this will be important later. What do I mean that the graph has symmetry? Where is the line of symmetry?)
 
What are the domain and range? (Even though we chose only a few x values, we could have chosen any, so x is all real values – but our range has some limitations!)
 
The vertex is called a minimum on this graph (label this in notes) – why does this make sense?
 
Example 2:
Make some predictions here – what can we predict about this graph? (opens down, and has a y-int of 3 – should look like a Frisbee going up in the air and coming back down)
We can also look to the problem for help in choosing x values – in this problem the equation represents a story – what values would make sense for x? (only positive ones, since we aren’t going to worry about negative seconds)
Domain looks like all real numbers x, and it would be for the equation, but for this STORY we are limited to numbers from zero to when it hits the groun
Range also looks like all real numbers but what would it actually be?
Vertex is a what? (maximum!)
 
QUICK WRITE:
Do you think quadratic functions have a slope? Explain your reasoning.
(No, they don’t have a constant rate of change – the slope changes – from positive to negative or vice-versa – THIS IS CALCULUS!!!)
 
PARTNERS – two guided examples, approx 6 mins (don’t worry too much about the vocab – tell them to look in the book if they want, or take their best guess)
 
Example 3:
Have a student read – write the formula large off to the side – this can help you find the center of the graph – which can save you a LOT of time!!!
A) use the formula – have students give values – so x = -1 is our line of symmetry (sketch on graph)
B) I know that the vertex will be on this line, so I can substitute -1 for x to find the y value (plot this point)
C) max because this graph will open down (a is negative)
D) so we are going to make our table smart – put the vertex in the middle and then find a few more points – zero and one are easy, and the points on the other side must be the same because of symmetry
 
 
 
Key questions to ask during GP: (Question Script) 
 
 
IP
 
Clicker – four multiple choice problems
** interrupt to discuss good test-prep strategy for these questions
 
IP from textbooks
 
 
 
 
 
Closure: How will you close the lesson? 
 
Raffle tickets for productive IP
Share answers/questions from IP
 
How do you graph a quadratic function?
How can you use the line of symmetry to help you?
 
Assessment: How will you assess mastery of the objective?
  • EXIT TICKET
 
Homework
 
 
Anticipated Challenges
 
 
 
 
Reflection: This is a pretty long lesson. I have two hour blocks, so it was possible – but I would consider splitting this into two lessons – one for just graphing, and the next for the axis of symmetry/vertex.

Lesson Resources

10 2 EX  
638
10 2 DN  
406
10 2 packet graphing quadratics  
1,084

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