MA19.A1.9

Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.9
Select an appropriate method to solve a quadratic equation in one variable.

Unpacked Content

Knowledge

Students know:

Any real number has two square roots, that is, if a is the square root of a real number then so is -a.
The method for completing the square.
Notational methods for expressing complex numbers.
A quadratic equation in standard form (ax²+bx+c=0) has real roots when b²-4ac is greater than or equal to zero and complex roots when b²-4ac is less than zero.

Skills

Students are able to:

Accurately use properties of equality and other algebraic manipulations including taking square roots of both sides of an equation.
Accurately complete the square on a quadratic polynomial as a strategy for finding solutions to quadratic equations.
Factor quadratic polynomials as a strategy for finding solutions to quadratic equations.
Rewrite solutions to quadratic equations in useful forms including a ± bi and simplified radical expressions.
Make strategic choices about which procedures (inspection, completing the square, factoring, and quadratic formula) to use to reach a solution to a quadratic equation.

Understanding

Students understand that:

Solutions to a quadratic equation must make the original equation true and this should be verified.
When the quadratic equation is derived from a contextual situation, proposed solutions to the quadratic equation should be verified within the context given, as well as mathematically.
Different procedures for solving quadratic equations are necessary under different conditions.
If ab=0, then at least one of a or b must be zero (a=0 or b=0) and this is then used to produce the two solutions to the quadratic equation.
Whether the roots of a quadratic equation are real or complex is determined by the coefficients of the quadratic equation in standard form (ax²+bx+c=0).

Vocabulary

Completing the square
Quadratic equations
Quadratic formula
Inspection
Imaginary numbers
Binomials
Trinomials

Aligned Learning Resources

Difference of Squares

Perfect Square Factorization Introduction

Factoring Perfect Squares

Factoring Simple Quadratics Review

Factoring Quadratics in Any Form

KutaSoftware: Algebra 1 - Factoring Quadratic Polynomials Easy Part 1

How Many Solutions?: Algebra 1, Episode 14: Unit 7, Lesson 5 | Illustrative Math

Solving Quadratic Equations With the Zero Product Property: Algebra 1, Episode 13: Unit 7, Lesson 4 | Illustrative Math

Completing the Square (Part 1): Algebra 1, Episode 20: Unit 7, Lesson 12 | Illustrative Math

Rewriting Quadratic Expressions in Factored Form (Part 1): Algebra 1, Episode 15: Unit 7, Lesson 6 | Illustrative Math

Rewriting Quadratic Expressions in Factored Form (Part 2): Algebra 1, Episode 16: Unit 7, Lesson 7 | Illustrative Math

Rewriting Quadratic Expressions in Factored Form (Part 3): Algebra 1, Episode 17: Unit 7, Lesson 8 | Illustrative Math

Solving Quadratic Equations by Using Factored Form: Algebra 1, Episode 18: Unit 7, Lesson 9 | Illustrative Math

What Are Perfect Squares?: Algebra 1, Episode 19: Unit 7, Lesson 11 | Illustrative Math

Applying the Quadratic Formula (Part 1): Algebra 1, Episode 24: Unit 7, Lesson 17 | Illustrative Math

Changing Elevation

Character Study: Scout Finch

Character Traits: Rise and Shine: Literacy Time

Classifying Quadrilaterals

Classroom Connection: Are You a Square?

Show Not Tell: Similes: Camp TV

Slope and House Construction

Text Structures

The Art of Math

The Case of the Missing Theme: Take the Stage

The Constructed Languages of JRR Tolkien | It's Lit!

The Electric Company Math Activities: Measure to Compare

The Electric Company Math Activities: Skip Counting 5, 10, and 100

Finding the Zeros by Graphing

Mondrian Factoring Models

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