High School Math Guide

Quadratic Functions

Unit 1

MATH CORE STANDARDS II.F.BF.1 : Write a quadratic or exponential function that describes a relationship between two quantities. II.A.SSE.1 : Interpret expressions that represent a quantity in terms of its context. II.A.CED.2 : Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. II.F.LE.3 : Observe suing graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. II.F.IF.9 : Compare properties of two functions, each represented a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). II.F.IF.6 : Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph. II.F.IF.4 : For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. II.F.IF.5 : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Focus on quadratic functions; compare with linear and exponential functions. Critical Background Knowledge • 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) • Recognize sequences as functions (I.F.IF.3) • Distinguish between and construct linear and exponential functions (I.F.LE.2) • Understand that rewriting an expression can highlight quantities (7.EE.2) • Determine rate of change and initial value of a function (8.F.3, 8.F.4) • Interpret unit rate as the slope (8.EE.5) • Create and graph linear and exponential equations, labeling axes and scale (I.A.CED.2) • Choose appropriate scales and label a graph (I.N.Q.1, I.N.Q.2) • Construct a function to model a linear relationship between two quantities (8.F.4) • Describe qualitatively the relationship between two quantities by analyzing a graph (8.F.5) • Observe using graphs and tables a quantity increasing exponentially eventually exceeds a quantity increasing linearly (I.F.LE.3) • Distinguish between linear and exponential functions (I.F.LE.1, I.F.LE.2) • Compare properties of two functions using multiple representations (I.F.IF.9) • Compare properties of two functions (linear to linear), each represented in a different way (8.F.2) • Find intercepts, rates of change, and end behavior (I.F.IF.4) • Calculate and interpret the rate of change of a linear or exponential function (I.F.IF.6) • Determine the rate of change from a description of a relationship or from two (x, y) values and interpret its meaning (8.F.4)