Unpacked Content
Knowledge
Students know:
- Techniques for generating equivalent forms of an algebraic expression, including factoring and completing the square for quadratic expressions and using properties of exponents.
- When one form of an algebraic expression is more useful than an equivalent form of that same expression to solve a given problem.
Skills
Students are able to:
- Use algebraic properties including properties of exponents to produce equivalent forms of the same expression by recognizing underlying mathematical structures.
- Factor quadratic expressions.
- Complete the square in quadratic expressions.
- Use the vertex form of a quadratic expression to identify the maximum or minimum and the axis of symmetry.
Understanding
Students understand that:
- Making connections among equivalent expressions reveals the roles of important mathematical features of a problem.
Vocabulary
- Quadratic expression
- Zeros
- Complete the square
- Roots
- Zeros
- Solutions
- x-intercepts
- Maximum value
- Minimum value
- Factor
- Roots
- Exponents
- Equivalent form
- Vertex form of a quadratic expression
