A.SSE.3b: Revealing Function's Extrema through Completing the Square in Quadratic Expression

Grade: Algebra

Domain: SSE: Seeing Structure in Expressions

Standard Description

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Domain Description

Parts of an expression, such as terms, factors, and coefficients can be interpreted individually. Complex expressions can be understood by viewing parts of it as a single unit. Through the structure of an expression, you can identify and implement rewrites. Recognition of patterns, like a difference of squares, can aid in this. Quadratic expressions can be factored to reveal the zeros of the function, or completed to reveal its maximum or minimum values. Exponential functions can be transformed using exponent properties. Similarly, the formula for a finite geometric series sum can be derived and applied to solve problems like mortgage payments.