Section 5: Quadratic Equations and Functions

If additional assistance is needed, tutoring is available.  Students are also encouraged to watch Algebra Nation videos, or view lesson regarding the topic on Khan Academy.  Students are provided additional practice on an as needed basis depending on topic needing enhancement  Remind is available to parents as well as students for after school hours assistance directly from me.

All IEP accommodations for each student will be provided in class on an as needed basis.

TeacherIvette Pujol
Subject AreaMath: Algebra 1
Grade LevelAlgebra 1 Honors 7th & 8th Grade
Week #
Unit of InstructionSection 5 Quadratic Equations and Functions
Standard(s) Taught

MAFS.912.A-SSE.1.2:  Use the structure of an expression to identify ways to rewrite it.

MAFS.912.A-REI.2.4a,b:  Solve quadratic equations in one variable.

    a.  Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

    b. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

MAFS.912.A-CED.1.1:  Create equations and inequalities in one variable and use them to solve problems.

Learning Targets and Learning Criteria

Students are successful when they can:

  • solve quadratic equations by inspection, finding square roots, completing the square, quadratic formula, and factoring.
  • explain why taking the square root of both sides when solving a quadratic equation will yield two solutions.
  • use pictures, algebra tiles, and/or symbols to explain the concept underlying completing the square.
  • derive the quadratic formula by completing the square of ax2+bx+c.
  • determine the best method to solve a quadratic equation in one variable.
Classroom Activities

Warm Up: Quadratic Equations and Functions – Part 1

Solving Quadratic Equations by Completing the Square – Review of:

  • Difference of Two Squares
  • Perfect Square Trinomials
  • Solving Quadratic by Taking the Square Root
  • Completing the Square

Introduction of New Material:  Solving Quadratics by Completing the Square

Some quadratic expressions can be factored as perfect squares. For example, x²+6x+9=(x+3)². However, even if an expression isn’t a perfect square, we can turn it into one by adding a constant number. For example, x²+6x+5 isn’t a perfect square, but if we add 4 we get (x+3)². This, in essence, is the method of *completing the square.

Algebra Nation Work Sheet:

CW and HW: IXL BB.9 Solving Quadratic Equations by Completing the Square

Solve by completing the square.

u2 + 28u + 9 = 0

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

u =  or u = 

 

Assignments Due

Week of 02/11/19:

Classwork and Homework assignments this week:

IXL Assignments:

SKILL: A1-BB.5 Solve a quadratic equation using square roots – 70 % Mastery

SKILL: A1-BB.8 Complete the square – 90 – 100% Mastery

SKILL: A1-BB.9 Solve a quadratic equation by completing the square – 70% Mastery
 

 

Additional Resources

Algebra Nation Quadratic Equations and Functions

www.khanacademy.org/math/algebra/quadratics/solving-quadratics-by-completing-the-square