High School Math Guide

Structures of Quadratic Expressions

Unit 2

MATH CORE STANDARDS II.F.IF.7 : Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. II.F.BF.3 : Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. II.F.IF.8 : Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. II.F.BF.1 : Write a quadratic or exponential function that describes a relationship between two quantities. II.A.SSE.3 : Chose and produce an equivalent form of an expressions to reveal and explain properties of the quantity represented by the expression. II.A.SSE.2 : Use the structure of an expression to identify ways to rewrite it. Critical Background Knowledge • Understand absolute value as a distance from 0 on a number line (6.NS.7c) and solve absolute value equations (8.EE.7c) • Graph linear and exponential functions showing key features (I.F.IF.7) • Interpret key features of a graph (I.F.IF.4) • Identify and use transformations of functions (I.F.BF.3) • Identify the effect of vertical translations of graphs of linear and exponential functions on their equations (I.F.BF.3) • Use geometric descriptions of rigid motions to transform figures and predict the effect of transformation (I.G.CO.6) • Graph functions with and without technology (I.F.IF.7) • 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) • Apply properties of integer exponents to generate equivalent numerical expressions (8.EE.1) • Perform operations with number expressed in scientific notation (8.EE.4) • Understand exponential growth or decay as the constant percent rate per unit interval (I.F.LE.1c) • Determine an explicit expression, a recursive process, and combine standard function types (I.F.BF.1) • Write arithmetic and geometric sequences both recursively and with an explicit formula (I.F.BF.2) • Use function notation (I.F.IF.2) Continued on next page