Reflection: Students with Disabilities Vertex Form to Standard Form  Section 3: Discussion & Closing
It is usually a few lessons after this one that I realize students are confused about going from vertex to standard form. At the end of this lesson they usually seem to have a firm grasp of what to do. But once I introduce going from standard form to vertex form, they seem to be confused when we spiral back to this content. This year, I've tried a few different things to help struggling students master vertex to standard form.
First, I think it helps some students to generate a list of steps. Although it may seem superfluous initially, when they start to work in the opposite direction their written steps may help them be clear about what they're doing.
Second, I try to revisit this content in warm up activities, especially when we're learning to complete the square. I want students to remember that going from vertex to standard form is its own, separate task.
Lastly, I try to remind students that they are really just simplifying an equation here by following the order of operations. I often see students try to adjust the constant term when going from vertex to standard form, an idea they have picked up from going the other direction. I try to encourage them to just follow the algebra here, rather than thinking about it too much! There's plenty of thinking to do when they go from standard to vertex form.
Vertex Form to Standard Form
Lesson 7 of 18
Objective: SWBAT use an area model to square binomials. Students will be able to rewrite quadratic functions from vertex form into standard form.
Opening
I begin class with a warm up activity where students are first asked to identify parameters "a," "b," and "c" for a quadratic and then multiply some simple binomials. This multiplying binomials piece is a review of what students have been working on and I have a few students come to the board to show their area models. Students work up to Question #8 as part of the warm up for class. These warm up questions give students a chance to revisit and solidify what they learned in the last lesson and give me the opportunity to check for understanding. From a quick look at the warm up, I can identify students who need targeted instruction in multiplying binomials, or who might need more scaffolding when it comes to factoring later in the unit.
Next, I tell students that today’s task will focus on applying these new multiplication skills to change quadratic functions that are in vertex form into standard form. I also like to emphasize with students that it is important for them to be able to work fluidly between quadratics in different forms. Today we will be working from the vertex to the standard form, and later in the unit, we will go in the opposite direction.
Resources (1)
Resources (1)
Resources
Investigation
I like to group students in homogeneous groups of three to four students for this activity. I hand out the Vertex to Standard Form ask and we read through the assignment together. A good place to start is on Question #10 where students see a quadratic in vertex form (where k = 0). I might do Questions 10 and 11 as a whole group and then let students start on Question #12 in their small groups.
Students first have to think about how "k" affects the number of xintercepts a quadratic will have. I like how this portion of the task connects the vertex form further with xintercepts which is where we are headed as a class. Next, students graph quadratics in vertex form. I emphasize that students should graph at least three points on both sides of the vertex. Of course, students will start to remember about the symmetry of quadratics and graph accordingly. Finally, I ask students to put each of those vertex form equations (the ones they just graphed) into standard form.
Things I look for while students work:
 Students who struggle to recognize the effects of k may need help sketching some basic graphs to see how many xintercepts result with a change in k.
 Some students in my class with inevitably have difficulty graphing the quadratics in vertex form. They may need prompting to remember how to identify the vertex and then a hint about using that as the starting point to the graph and looking at points on either side. I encourage them to make a table in order to graph their points.
 Sometimes students need reassurance they can use the area model even if the constant term is negative. I try to help them construct a diagram that shows this.
 Students may struggle with the order of operations in Question 20. They may need reminding to square the binomial first and then use the Distributive Property to multiply each term in the resulting trinomial. Finally, they will add the constants at the end.
Resources (1)
Resources (1)
Resources
Discussion & Closing
Discussion
I try to leave ample time to discuss this activity. I have students who finish early share some of their graphs and standard form equations on the board.
I always find that graphing quadratics is a good way to incorporate the SMP7: Look for and make use of structure. In my discussion of both Questions 12 through 17 and 18 through 23 we can talk about why the graphs come out the way they do. Students should be able to see the effect of parameter k on the xintercepts and of the x squared on the shape of the parabola. I believe actually having students plot points helps in this understanding.
Next, we discuss how to turn these vertex form equations into standard form. Some students may struggle with following the general rules of the order of operations. I try to elicit from students what order we need to do things in and how to think about a negative sign out in front of the parenthesis. Students may need reminders about the distributive property, but most of the guidance and corrections can come from other students in the class, rather than me.
Reflection
Have students complete an Exit Ticket related to Reflection. Ask them to complete the follow prompt on an index card:
Summarize what you have learned in writing: How would you summarize the steps for going from Vertex Form to Standard Form?
Resources (2)

Structures of Expressions 2.2 is licensed by © 2012 Mathematics Vision Project  MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons AttributionNonCommercialShareAlike 3.0 Unported license.
http://www.mathematicsvisionproject.org/secondarymathematicsii.html
Similar Lessons
Simplifying Rational Expressions, Day 2
Environment: Suburban
Quadratic Function Jigsaw
Environment: Suburban
Combining Like Terms
Environment: Urban
 UNIT 1: Introduction to Algebra: Focus on Problem Solving
 UNIT 2: Multiple Representations: Situations, Tables, Graphs, and Equations
 UNIT 3: Systems of Equations and Inequalities
 UNIT 4: Quadratics!
 UNIT 5: Data and Statistics
 UNIT 6: Arithmetic & Geometric Sequences
 UNIT 7: Functions
 LESSON 1: A Fireworks Display
 LESSON 2: Rabbit Run  Day 1 of 2
 LESSON 3: Rabbit Run  Day 2 of 2
 LESSON 4: Properties of Parabolas Day 1 of 2
 LESSON 5: Properties of Parabolas Day 2 of 2
 LESSON 6: Using an Area Model to Multiply Binomials
 LESSON 7: Vertex Form to Standard Form
 LESSON 8: Standard Form to Vertex Form Day 1 of 2
 LESSON 9: Standard Form to Vertex Form Day 2 of 2
 LESSON 10: Where Will the Rocket Land? Putting it all Together
 LESSON 11: Completing the Square Methods & Practice
 LESSON 12: Factoring Day 1 of 2
 LESSON 13: Factoring Day 2 of 2
 LESSON 14: Choosing a Method to Find xintercepts
 LESSON 15: Quadratics Portfolio Day 1 of 3
 LESSON 16: Quadratics Portfolio Day 2 of 3
 LESSON 17: Quadratics Portfolio Day 3 of 3
 LESSON 18: Is It a Home Run?