Quadratic Functions

In unit A1 students developed fluency with linear functions and in unit A2 they learned about simple exponential functions. Students can use graphing technology to plot a function, find intercepts and intersection points, and find a linear regression. They know exponent rules and the application of the distributive property to combining like terms or factoring out a common factor.

In this unit students build and interpret quadratic functions. They work with contexts that can be modeled by quadratic functions and compare them with contexts that can be modeled linear and exponential functions. They express quadratic functions using recursive equations (e.g. $f(n + 1) = f(n) + 2n + 1$), equations in two variables (e.g. $y = x^2 + 2x + 3$), or function notation (e.g. $f(x) = x^2+2x+3$). They understand the purpose of different forms for the quadratic expression on the right hand side in the last two cases. They graph quadratic functions expressed in different forms, and construct functions expressed in factored or vertex form for a given learn how to put a function in vertex form, and see what information can be most easily obtained from it.

In unit A4 students solve quadratic equations in one variable approximately and exactly using various methods. They continue to develop facility in algebraic manipulation of quadratic expressions and equations. In unit A5, they explore complex numbers and revisit quadratic equations to solve for complex roots.