MA19.8A.6
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
UP:MA19.8A.6
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
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.
