Download Solving Quadratic Trajectory

1. Functions &
relationships
2. Equivalent
expressions
Solving Quadratic Equations
Grade 7
Grade 8
Recognize simple
a. Describe, using words and symbols, and
quadratic
make sense of quadratic functions
relationships
represented using models, graphs, tables,
represented in graphs,
and equations (standard, vertex and
tables, and equations
factored forms) and understand how they
as one example of a
relate to a context (mathematical or real
non-linear
world).
relationship.
b. Compare properties of quadratics, such as
number of zeros or intervals of
increasing/decreasing, to other simple
functions (e.g., linear, inversely
proportional, and exponentials).
c. Connect elements of the graphic
representation of parabolas with each
symbolic representation - standard, vertex,
factored forms (e.g., vertex, axis of
symmetry, direction of opening, zeros, yintercept).
d. Identify and use variables and determine an
appropriate set of values for the
independent (domain) and dependent
(range) variables.
Evaluate expressions
a. Develop rules for manipulating symbolic
given values of the
expressions in ways that are both
variables and interpret
connected to and independent from
the meaning of
arithmetic operations (e.g., partial
solutions within given
products/distributive property, and
contexts.
combining integers) tabular, graphical and
contextualized reasoning.
b. Using a model (algebra tiles, area model),
translate among standard, factored, and
vertex forms given a leading coefficient of
1 or -1 and connect the model to symbolic
representations.
Algebra
a. Determine and explain whether a relationship
(given in contextual, symbolic, tabular, or
graphical form) is a function and identify its
domain and range.
b. Read, interpret, and use function notation.
c. Identify the intervals where the values of a
function/relation are positive or negative, and
describe the behavior of a function as x increases
or decreases, given the symbolic and graphical
representations. (linear, quadratic, exponential,
inverse, cubic, power, and polynomial).
d. Apply and graph given transformations to the
parent function y = x2 and represent symbolically.
a. Review and strengthen students’ understanding
of the conventional order of operations rules and
number properties in the contexts of practical
problems and evaluating expressions.
b. Express quadratic relations in a variety of forms
and translate among the various forms (standard,
factored, and vertex) and reason about which
form is most useful for a particular context.
Include completing the square.
c. Explain how the properties of associativity,
commutativity, and distributivity, as well as
identity and inverse elements, are used in
algebraic calculations.
Beyond
a. Identify the intervals where the values of a
function are positive or negative, and
describe the behavior of a function as x
approaches positive or negative infinity,
given the symbolic and graphical
representations. (power, polynomial,
logarithmic, trigonometric, rational, etc.)
b. Recognize whether a function (given in
tabular or graphical form) has an inverse and
recognize simple inverse pairs.
a. Find an equation of a circle given its center
and radius; given the equation of a circle find
its center and radius.
b. Graph ellipses and hyperbolas with axes
parallel to the x and y-axes, given equations.
c. Identify and distinguish among geometric
representations of parabolas, circles, ellipses,
and hyperbolas; describe their symmetries
and how they are related to cones.
Oakland Schools - DELTA Project
Solving Quadratic Equations Version 7
December 6, 2010
3.
Solve
4.
Data
analysis
a. Understand the
concept of and be
able to estimate
the square root and
the cube root of a
given value.
b. Given a real-world
context, estimate
solutions to simple
quadratic
equations by
inspecting their
graphs and tables.
a. Connect the concrete models and
“balancing” methods used to solve linear
equations to solve quadratic equations and
routinize methods for solving equations
symbolically.
b. Use tables, graphs, and equations of
quadratic relations to solve problems in a
variety of situations including geometry
(e.g., equations of circles), science, and
business.
c. Set up and graphically solve systems
involving linear and quadratic relationships
and interpret the meaning of the solution in
the real-world context.
d. Relate quadratic functions in standard,
factored, and vertex forms (with leading
coefficient of 1 or -1) to their graphs and
vice versa and understand why the
solutions to a quadratic equation are the xintercepts of the corresponding function.
Organize and summarize a data set in a table,
plot, chart, or spreadsheet; find patterns in a
display of data; understand and critique data
displays in the media.
a. Connect the method of “doing/undoing” used to
solve linear equations to solve quadratic
equations and routinize methods for solving
equations.
b. Know that the imaginary number i is one of two
solutions to x2 = -1 and relate the number of real
solutions of a quadratic equation to the graph of
the associated quadratic function.
c. Associate a given equation with a function whose
zero(s) are the solutions of the equation and be
able to explain the meaning of the solution(s).
d. Set-up and solve quadratic equations/inequalities
and systems of linear/quadratic and
quadratic/quadratic equations/inequalities using
an appropriate strategy given the context (e.g.,
calculator approximation, completing the square,
and the quadratic formula).
e. Recognize that a quadratic in factored form is
composed of two linear factors and use this
knowledge to connect the solution of a linear
function to a related quadratic function.
a. Organize and summarize a data set in a table,
plot, chart, or spreadsheet; find patterns in a
display of data; understand and critique data
displays in the media.
b. Identify the function family best suited for
modeling a given real-world situation.
c. Use a calculator or computer software to find the
quadratic regression model for a set of data and
answer questions about the context (e.g.,
projectile motion and economic problems)
represented by the data.
a. Find and make sense of the zero’s of
polynomial function from its linear factors.
b. Determine the zeros of the numerator and
denominator of simple rational functions by
factoring, calculator approximation,
completing the square, or using the quadratic
formula.
c. Understand the relationship between the
zeros of the numerator and denominator of a
simple rational function and the function’s
intercepts, asymptotes, and domain.
d. Apply given transformations to parent
functions and represent symbolically.
e. Combine functions by addition, subtraction,
multiplication, and division.
a. Identify the function family best suited for
modeling a given real-world situation.
b. Use a calculator or computer software to find
the regression model for a set of data and
answer questions about the context (e.g.,
science and economic problems) represented
by the data.
Oakland Schools - DELTA Project
Solving Quadratic Equations Version 7
December 6, 2010