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Subjects
Grades
Resource Type
Common Core: Standard
Common Core: ELA
Common Core: Math
CCLS  Math: A.REI.4
 Category
 Reasoning With Equations And Inequalities
 SubCategory
 Solve Equations And Inequalities In One Variable
 State Standard:
 Solve quadratic equations in one variable.
20 Results

 Student Outcomes Students understand the Fundamental Theorem of Algebra; that all polynomial expressions factor into linear terms in the realm of complex numbers. Consequences, in particular, for...

 Student Outcomes Students solve quadratic equations with real coefficients that have complex solutions. Students extend polynomial identities to the complex numbers. Students note the difference...

 Student Outcomes Students solve quadratic equations with real coefficients that have complex solutions. They recognize when the quadratic formula gives complex solutions and write them as a + bi for...

 Student Outcomes Students understand the possibility that an equation—or a system of equations—has no real solutions. Students identify these situations and make the appropriate geometric...

 Students extend their facility with solving polynomial equations to working with complex zeros. Complex numbers are introduced via their relationship with geometric transformations. The topic...

 Student Outcomes Students develop facility with graphical interpretations of systems of equations and the meaning of their solutions on those graphs. For example, they can use the distance formula to...

 Student Outcomes Students solve systems of linear equations in two variables and systems of a linear and a quadratic equation in two variables. Students understand that the points at which the two...

 Student Outcomes Students solve simple radical equations and understand the possibility of extraneous solutions. They understand that care must be taken with the role of square roots so as to avoid...

 Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions.

 Students solve polynomial, rational, and radical equations, and apply these types of equations to realworld situations. They examine the conditions under which an extraneous solution is introduced...

 Students apply their experiences from Topic A as they transform quadratic functions from standard form to vertex form, (x) = a(x  h)2 + k in Topic B. The strategy known as completing the square is...

 Topic A introduces polynomial expressions. In Module 1, students learned the definition of a polynomial and how to add, subtract, and multiply polynomials. Here, their work with multiplication is...

 Student Outcomes Students use the quadratic formula to solve quadratic equations that cannot be easily factored. Students understand that the discriminant, b2  4ac, can be used to determine whether...

 Student Outcomes Students derive the quadratic formula by completing the square for a general quadratic equation in standard form, ax2 + bx + c = 0, and use it to verify the solutions for equations...

 Student Outcomes Students solve complex quadratic equations, including those with a leading coefficient other than 1, by completing the square. Some solutions may be irrational. Students draw...

 Student Outcomes Students rewrite quadratic expressions given in standard form, ax2 + bx + c (with a ≠ 1), as equivalent expressions in completed square form, a(x  h)2 + k. They build quadratic...

 Student Outcomes Students rewrite quadratic expressions given in standard form, ax2 + bx + c (with a = 1), in the equivalent completedsquare form, a(x  h)2 + k, and recognize cases for which...

 Student Outcomes Students use appropriate and efficient strategies to find solutions to basic quadratic equations. Students interpret the verbal description of a problem and its solutions in context...

 Student Outcomes Students learn that equations of the form (x  a)(x  b) = 0 have the same solution set as two equations joined by “or:” x  a = 0 or x  b = 0. Students solve factored or easily...

 Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions In earlier modules, students analyze the process of solving equations and developing fluency in writing,...