High School Math Guide

Solving Quadratic Equations

Unit 3

MATH CORE STANDARDS II.N.RN.1 : Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to show values, allowing for a notation for radicals in terms of rational exponents. II.N.RN.2 : Rewrite expressions involving radicals and rational exponents using the properties of exponents. II.A.REI.4 : Solve quadratic equations in one variable. II.A.REI.7 : Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. II.A.CED.1 : Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. II.N.CN.7 : Solve quadratic equations with real coefficients that have complex solutions. II.N.CN.8 : Extend polynomial identities to the complex numbers. Limit to quadratics with real coefficients. II.N.CN.9 : Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. II.N.RN.3 : Explain why sums and products of rational numbers are rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational. II.N.CN.1 : Know there is a complex number i such that i 2 = -1 , and every complex number has the form a +bi with a and b real. II.N.CN.2 : Use the relation i 2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Limit to multiplications that involve i 2 as the highest power of i . II.A.CED.3 : Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. • Properties of integer exponents (8.EE.1) • Work with radical and integer exponents (8.EE.1-4) • Identify when two expressions are equivalent (6.EE.4); understand that rewriting an expression in different forms can shed light on problems and how quantities are related (7.EE.2) • Understand exponential growth or decay as the constant percent rate per unit interval (I.F.LE.1c) • Apply properties of operations to generate equivalent expressions (6.EE.3) • Understand that rewriting an expression in different forms can shed light on the problem and how the quantities in it are related (7.EE.2) • Expand expressions using the distributive property (8.EE.7b) • Evaluate square roots of perfect squares (8.EE.2) and simplify radicals (8.NS.3) • Apply properties of operations to distribute and factor to create equivalent expressions (6.EE.3, 7.EE.1) • Solve equations (6.EE.7, 7.EE.4a, 8.EE.7) Continued on next page… Critical Background Knowledge