Math 20-1
Quadratics Outcomes
Relations and Functions Outcome 1- Factor polynomial expressions of the form:

ax 2  bx  c, a  0

a 2 x 2  b2 y 2 , a  0, b  0

a( f ( x))2  b( f ( x))  c, a  0

a2 ( f ( x))2  b ( g ( y)), a  0, b  0
2
Proficiency
4
3
2
1
Criteria
- Fully factor a polynomial expression that has a quadratic pattern,
including: a(f(x))2+b(f(x))+c, a≠0 and a2(f(x))2+b2(f(x))2+c, a≠0, b≠0
where f(x) and g(y) is a binomial
- Fully factor a polynomial expression that has a quadratic pattern,
including: a(f(x))2+b(f(x))+c, a≠0 and a2(f(x))2+b2(f(x))2+c, a≠0, b≠0
where f(x) and g(y) is a monomial
- Partially factor a polynomial expression that has a quadratic pattern,
including: a(f(x))2+b(f(x))+c, a≠0 and a2(f(x))2+b2(f(x))2+c, a≠0, b≠0
where f(x) and g(y) is a monomial
- Cannot partially factor a polynomial expression that has a quadratic
pattern, including: a(f(x))2+b(f(x))+c, a≠0 and a2(f(x))2+b2(f(x))2+c, a≠0,
b≠0 where f(x) and g(y) is a monomial
Relations and Function Outcome 3- Analyze quadratic functions of the form y=a(x-p)2+q and determine:
 Vertex
 Domain and range
 Direction of opening
 Axis of symmetry
 x and y intercepts
Proficiency
Criteria
- Given a quadratic in the form y=a(x-p)2+q, determine the vertex,
domain and range, direction of opening, axis of symmetry and x and y
4
intercepts of a nonroutine problem
- Compare and determine the effects of a,p,q on a quadratic function
- Given a quadratic in the form y=a(x-p)2+q, determine the vertex,
domain and range, direction of opening, axis of symmetry and x and y
3
intercepts of a routine problems
- Compare and determine the effects of a,p,q on a quadratic function
- Given a quadratic in the form y=a(x-p)2+q, identify the vertex, domain
and range, direction of opening, axis of symmetry and determine x
2
and y intercepts of a routine problems
- Cannot compare or determine the effects of a,p,q on a quadratic
- Given a quadratic in the form y=a(x-p)2+q, cannot identify the vertex,
domain and range, direction of opening, axis of symmetry and
1
determine x and y intercepts of a routine problems
- Cannot compare or determine the effects of a,p,q on a quadratic
*note* Nonroutine in this case may mean a problem with an unfamiliar context or multistep.
Relations and Functions Outcome 4- Analyze quadratic functions of the form y=ax2+bx+c to identify
characteristics of the corresponding graph, including:
 Vertex
 Domain and range
 Direction of opening
 Axis of symmetry
 x and y intercepts
Proficiency
Criteria
- Write the quadratic function given in the form y=ax2+bx+c as a
quadratic function in the form y=a(x-p)2+q by completing the square
where b/a is not an integer
- Identify, correct, and explain errors in an example of completing the
4
square
- Write and solve a quadratic function that models a given situation for
non-routine problems
- Given a quadratic in the form y=ax2+bx+c, sketch and determine the
characteristics of the quadratic and explain the strategy used
- Write the quadratic function given in the form y=ax2+bx+c as a
quadratic function in the form y=a(x-p)2+q by completing the square
where b/a is an integer
- Identify, and correct errors in an example of completing the square
3
- Write and solve a quadratic function that models a given situation for
routine problems
- Given a quadratic in the form y=ax2+bx+c, sketch and determine the
characteristics of the quadratic and explain the strategy used
- Write the quadratic function given in the form y=ax2+bx+c as a
quadratic function in the form y=a(x-p)2+q by completing the square
where b/a is an integer with minor errors
- Identify errors and make minor mistakes in the correction of an
2
example of completing the square
- Write and solve a quadratic function that models a given situation for
routine problems with minor errors
- Given a quadratic in the form y=ax2+bx+c, sketch and determine the
characteristics of the quadratic and explain the strategy used
- Cannot write the quadratic function given in the form y=ax2+bx+c as a
quadratic function in the form y=a(x-p)2+q by completing the square
where b/a is an integer with minor errors
- Cannot identify errors and make minor mistakes in the correction of
an example of completing the square
1
- Cannot write and solve a quadratic function that models a given
situation for routine problems with minor errors
- Given a quadratic in the form y=ax2+bx+c, cannot sketch and
determine the characteristics of the quadratic and explain the
strategy used
Relations and Functions Outcome 5- Solve problems that involve quadratic equations.
Proficiency
4
3
2
1
Criteria
- Select a method for solving a quadratic equation, apply the method,
provide justification, and verify the solution
- Identify correct, and explain errors in a solution to a quadratic
equation
- Solve non-routine problems by determining and analyzing a quadratic
equation
- Select a method for solving a quadratic equation, and apply the
method, and verify the solution
- Identify and correct errors in a solution to a quadratic equation
- Solve routine problems by determining and analyzing a quadratic
equation
- Select a method for solving a quadratic equation, and apply the
method, and verify the solution with minor errors
- Identify errors and make minor mistakes in the correction of a
solution to a quadratic equation
- Solve routine problems by determining and analyzing a quadratic
equation with minor errors
- Cannot select a method for solving a quadratic equation, and apply
the method, and verify the solution with minor errors
- Cannot identify errors and make minor mistakes in the correction of a
solution to a quadratic equation
- Cannot solve routine problems by determining and analyzing a
quadratic equation with minor errors