Learning Goal: Develop procedural fluency with quadratics and transformations.
- Common Core
- HSA.REI.B.4.B – Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
- 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.
- HSF.IF.C.7.A – Graph linear and quadratic functions and show intercepts, maxima, and minima.
- TEKS (2015-16)
- A.3(E) – determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d
- 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(A) – solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula