Algebra 1 Online!
Henrico County Public Schools, Virginia
 Home Pacing - Middle School Pacing - High School SOL Tracker Algebra 1 Standards Virginia Department of Education Return to HCPS Math Courses
 Expressions and Operations Equations and Inequalities Functions Statistics SOL Review Materials Frequently Asked Questions
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 y-intercepts.
 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 x-intercept or a zero of a function f if and only if f(x) = 0.
Vertical Articulation
1. SOL 7.12 - represent relationships with tables, graphs, rules, and words
2. SOL 8.14 - make connections between any two representations (tables, graphs, words, rules)
3. SOL 8.17 - identify domain, range, independent/dependent variable
4. 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
5. SOL AFDA.4 - transfer between/analyze multiple representations of functions (algebraic formulas/ graphs/ tables/words)
6. 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
1. VDOE ESS Lesson: Functions 2 - Functions (PDF) - Investigating domain, range, intercepts, and zeros (Word)
2. 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)
3. Notes: Zeros and Intercepts (doc) | Answer Key (pdf)
Real World Lessons
Practice
Self-Assessments
Skills
Videos
Explore Learning
1. 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.
2. 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.
3. 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
1. Interactive: Slope Slider - manipulate a linear function in the form of f(x) = mx + b at Shodor.org
2. Interactive: Graphing Activity - real world activity and lesson used with graphing functions
3. Interactive: Exploring Standard Form - mathlet from GeoGebra