Unpacked Content
Knowledge
Students know:
- The vertex form of a quadratic expression asf (x) = a(x
- h)2 + k, where (h, k) is the vertex of the parabola.
- 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 with leading coefficient of one
- Complete the square in quadratic expressions.
Understanding
Students understand that:
- An expression may be written in various equivalent forms.
- Some forms of the expression are more beneficial for revealing key properties of the function.
Vocabulary
- Function
- zero of a function
- Roots
- parabola
- vertex form of a quadratic expression
- Minimum and maximum value
- Axis of symmetry
- Completing the square
- Exponential growth and decay
