- Assessment Limits :
In items that require the student to transform a quadratic equation to
vertex form, b/a must be an even integer.
In items that require the student to solve a simple quadratic equation
by inspection or by taking square roots, equations should be in the
form ax² = c or ax² + d = c, where a, c, and d are rational numbers and
where c is not an integer that is a perfect square and c – d is not an
integer that is a perfect square.
In items that allow the student to choose the method for solving a
quadratic equation, equations should be in the form ax² + bx + c = d,
where a, b, c, and d are integers.
Items may require the student to recognize that a solution is nonreal
but should not require the student to find a nonreal solution.
- Calculator :
- Clarification :
Students will rewrite a quadratic equation in vertex form by
completing the square.
Students will use the vertex form of a quadratic equation to complete
steps in the derivation of the quadratic formula.
Students will solve a simple quadratic equation by inspection or by
taking square roots.
Students will solve a quadratic equation by choosing an appropriate
method (i.e., completing the square, the quadratic formula, or
Students will validate why taking the square root of both sides when
solving a quadratic equation will yield two solutions.
Students will recognize that the quadratic formula can be used to find
- Stimulus Attributes :
The formula must be given in the item for items that can only be
solved using the quadratic formula.
Items should be set in a mathematical context.
Items may use function notation.
- Response Attributes :
Items may require the student to complete a missing step in the
derivation of the quadratic formula.
Items may require the student to provide an answer in the form
(x – p)² = q.
Items may require the student to recognize equivalent solutions to
the quadratic equation.
Responses with square roots should require the student to rewrite
the square root so that the radicand has no square factors.