Pg. 32/71 Homework HWPg. 69 – 71#17, 30 – 32, 69 – 82 Pg. 56#1 – 25 odd #55I would accept: C(t) = (INT(t)) or C(t) = (t) or C(t) = (t – 1) #56t > 0#575 < t < 6 #58s = -16t t + 10#59QI #60t = 2.73 sec, 6.65 sec #63D: (-∞, ∞) R: (-∞, ∞)#64 D: (-∞, ∞) R: (-∞, ∞) #65D: (-∞, ∞) R: (-2, ∞)#66 D: (-∞, ∞) R: (0, ∞) #67D: (-∞, 3)U(3,∞) R: {2, -2} #68 D: (-∞, ∞) R: (-∞, ∞)

1.5 Quadratic Functions and Geometric Transformations What transformations have you already learned? Horizontal Shift – Move opposite of what the value says (when it’s inside with the x) left or right on the x – axis. Vertical Shift – Move exactly what the value says (when it’s outside of the x) up or down on the y – axis. Reflection – Flip the function over the x – axis if the leading coefficient is negative. Vertical Stretch/Shrink – If the leading coefficient is larger than 1 the graph will shrink (get skinny). – If the leading coefficient is between 0 and 1 the graph will stretch (get fat).

1.5 Quadratic Functions and Geometric Transformations All these can be combined together into one basic formula. Vertex Formula of a Quadratic: What is the line of symmetry? The graph is: – Reflected about the x – axis if a is negative – Shifted h units to the right or left – Shifted k units up or down – Stretched if 0 < a < 1 – Shrunk if a > 1 To keep ourselves consistent, we will call all of the a values a stretch, as a shrink can be considered a type of stretch

1.5 Quadratic Functions and Geometric Transformations Graph the following equations without your calculator. State the domain and range.

Review What are the solutions of: y = f(x) y > f(x) 0 = f(x) 0 > f(x) Find the domain and range of the following: