Seeing Structure in Expressions
|Interpret the structure of expressions. [Quadratic and exponential]|
|1. Interpret expressions that represent a quantity in terms of its context.|
|a. Interpret parts of an expression, such as terms, factors, and coefficients.|
|b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret
P(1 + r)n as the product of P and a factor not depending on P.
|2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it
as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
|Write expressions in equivalent forms to solve problems. [Quadratic and exponential]|
|3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the
|a. Factor a quadratic expression to reveal the zeros of the function it defines.|
|b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.|
|c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can
be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.