A.7cd 
The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including
c) zeros of a function; and
d) x and yintercepts. 

Essential Knowledge and Skills 
 Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.
 For each x in the domain of f, find f(x).
 Represent relations and functions using concrete, verbal, numeric, graphic, and algebraic forms. Given one representation, students will be able to represent the relation in another form.
 Detect patterns in data and represent arithmetic and geometric patterns algebraically.

Essential Understandings 
 Graphs can be used as visual representations to investigate relationships between quantitative data.
 Inductive reasoning may be used to make conjectures about characteristics of function families.
 An object x in the domain of f is an xintercept or a zero of a function f if and only if f(x) = 0.


Vertical Articulation 
 SOL 7.12  represent relationships with tables, graphs, rules, and words
 SOL 8.14  make connections between any two representations (tables, graphs, words, rules)
 SOL 8.17  identify domain, range, independent/dependent variable
 SOL AFDA.1  investigate/analyze function (linear/quadratic exponential/log) families/ characteristics: a) continuity; b) local/abs max/min;
c) domain/range; d) zeros; e) intercepts; f) intervals of increasing/ decreasing; g) end behaviors; h) asymptotes
 SOL AFDA.4  transfer between/analyze multiple representations of functions (algebraic formulas/ graphs/ tables/words)
 SOL AII.7  investigate/analyze functions (algebraically/ graphically) a) domain/range; b) zeros; c) x‐ and y‐intercepts; d) intervals of increasing/decreasing; e) asymptotes; f) end behavior; g) inverse of a function; h) composition of multiple functions

Instructional Materials 
 VDOE ESS Lesson: Functions 2  Functions (PDF)  Investigating domain, range, intercepts, and zeros (Word)
 VDOE ESS Lesson: Factoring for Zeros  Functions, Equations and Inequalities (PDF)  Relating the roots (zeros) of a quadratic equation and the graph of the equation (Word)
 Notes: Zeros and Intercepts (doc)  Answer Key (pdf)

Real World Lessons 

Practice 
 A.7bcdef  VDOE ESS: Exploring Functions (pdf)
 A.7c  VDOE ESS: Factoring for Zeros Worksheet (pdf)
 Worksheet: Zeros and Intercepts CW (doc)
 Worksheet: Zeros and Intercepts HW (doc)
 ExamView Quiz: X and Yintercepts

SelfAssessments 
 SOL Mini Quiz

Skills 
 JMU Pivotal Question: Zeros of a Quadratic (doc)
 JMU Pivotal Question: yIntercepts of a Quadratic (doc)
 JMU Pivotal Question: xIntercepts of a Quadratic (doc)

Videos 
 Video: PH Finding X and YIntercepts Using Standard Form
 Video: PH Graphing Using Intercept

Explore
Learning 
 Quadratics in Factored Form  Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.
 Roots of a Quadratic  Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
 Points, Lines, and Equations  Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change.

Websites 
 Interactive:
Slope Slider  manipulate a linear function
in the form of f(x) = mx + b at Shodor.org
 Interactive:
Graphing Activity  real world activity
and lesson used with graphing functions
 Interactive: Exploring Standard Form  mathlet from GeoGebra

Old Website Links 

Common Core
Standards 
8.F.3 
8.F.4 
8.F.5 
AAPR.3 
FIF.1 
FIF.2 
FIF.4 
FIF.5 
FIF.7a 
FIF.7c 
FIF.9 
FBF.1a 
FBF.1b 
FBF.3 
FLE.2 
FLE.5 
