Algebra 2
Unit 1 - Quadratics revisited
Unit 1: Students will revisit solving quadratic equations in this unit. Students explore relationships between number systems: whole numbers, integers, rational numbers, real numbers, and complex numbers. Students will perform operations with complex numbers and solve quadratic equations with complex solutions. Students will also extend the laws of exponents to rational exponents and use those properties to evaluate and simplify expressions containing rational exponents.
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To kick off the year, we will practice our skills at equation solving, before beginning Honors Advanced Algebra/Algebra 2.
The following are some videos to remind you how to solve equations. Please view these videos at your convenience.
The following are some videos to remind you how to solve equations. Please view these videos at your convenience.
What is & why 'i'?
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Standards
Perform arithmetic operations with complex numbers.
MGSE9-12.N.CN.1 Understand there is a complex number i such that i^2 = −1, and every complex number has the form a + bi where a and b are real numbers.
MGSE9-12.N.CN.2 Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
MGSE9-12.N.CN.3 Find the conjugate of a complex number; use the conjugate to find the (REMOVE: absolute value (modulus) and) quotient of complex numbers.
MGSE9-12.N.CN.1 Understand there is a complex number i such that i^2 = −1, and every complex number has the form a + bi where a and b are real numbers.
MGSE9-12.N.CN.2 Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
MGSE9-12.N.CN.3 Find the conjugate of a complex number; use the conjugate to find the (REMOVE: absolute value (modulus) and) quotient of complex numbers.
+ & - complex numbers
complex conjugate
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* complex numbers
/ complex numbers
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Higher powers of 'i.'
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Complex numbers mixed practice with answers
Complex number mixed practice
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Extension graphing complex numbers
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Extension absolute value = modulus of complex numbers
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Quadratic equations
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Try your skill at identifying examples of quadratics
Use your exponential rules to practice
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Solving Quadratics: Square root method
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Try the practice to solve quadratics by taking square roots.
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Standards
Use complex numbers in polynomial identities and equations.
MGSE9-12.N.CN.7 Solve quadratic equations with real coefficients that have complex solutions by (but not limited to) square roots, completing the square, and the quadratic formula.
MGSE9-12.N.CN.8 Extend polynomial identities to include factoring with complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).
MGSE9-12.N.CN.7 Solve quadratic equations with real coefficients that have complex solutions by (but not limited to) square roots, completing the square, and the quadratic formula.
MGSE9-12.N.CN.8 Extend polynomial identities to include factoring with complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).
Solve equations and inequalities in one variable
MGSE9-12.A.REI.4 Solve quadratic equations in one variable.
MGSE9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation.
MGSE9-12.A.REI.4 Solve quadratic equations in one variable.
MGSE9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation.
The document 'how to solve quadratics 3 ways' will be referred to several days this week. Instructor Cortez has great notes and practice on three 3 methods for solving quadratic equations.
How to write a quadratic in standard form
Solving quadratics using completing the square
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Solving quadratics using the square root method
Solving quadratics using quadratic formula
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Extend the properties of exponents to rational exponents.
MGSE9-12.N.RN.1 Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.
MGSE9-12.N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
MGSE9-12.N.RN.1 Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.
MGSE9-12.N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Explanation for rational exponents
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Radical to rational to radical conversion
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Simplifying expressions with rational exponents
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