Reflection: Developing a Conceptual Understanding Comparing the Three Methods of Solving Quadratics - Section 1: Warm Up

I was very happy with the way this question went with the students.  Most students started by using the given quadratic formula to write down the a, b and c values and then worked backwards to plug these into a quadratic equation.  Some students finished earlier than others and I asked them to think about other ways the equation could have been written.  They had fun with this idea and came up with several examples of other equations.  Here are a few:

2x^2+10x=-3

10x=-2x^2-3

2x^2=-3-10x

While these are all simple algebraic manipulations, it was interesting for the students to see that all of these variations led to the same solutions.  I had various students post their ideas on the board so that the class could see all of the possibilities.

Working Backwards
Developing a Conceptual Understanding: Working Backwards

Comparing the Three Methods of Solving Quadratics

Unit 6: Quadratic Functions
Lesson 12 of 21

Big Idea: While several methods can sometimes be used to solve a quadratic equation, one method may be more efficient.

Print Lesson
5 teachers like this lesson
Standards:
Subject(s):
40 minutes

James Bialasik

Similar Lessons

The Factor Theorem & Synthetic Substitution
Algebra II » Cubic Functions
Big Idea: Synthetic substitution is an excellent tool that can be used strategically to help factor polynomials and identify zeros.
Favorites(3)
Resources(19)
Fort Collins, CO
Environment: Suburban

Sketching Graphs of Polynomial Functions
12th Grade Math » Polynomial and Rational Functions
Big Idea: Build upon existing knowledge of second and third degree functions to sketch graphs of other polynomial functions.
Favorites(3)
Resources(13)
Troy, MI
Environment: Suburban

Graphing Quadratic Functions (Day 2 of 2)
Algebra I » Quadratics
Big Idea: Students will graph more challenging quadratic functions using the zero product property and coordinate pairs.
Favorites(4)
Resources(18)
Washington, DC
Environment: Urban