Learning Goal: Introduce the features of quadratic functions and the effects when changing a, h, and k.
- Common Core
- HSF.BF.B.3 – Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
- A.6(A) – determine the domain and range of quadratic functions and represent the domain and range using inequalities
- A.7(A) – graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry
- A.7(C) – determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x – c), f(bx) for specific values o f a, b, c, and d
- A.8(B) – write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems