Review of Chapter 5 Pre Calculus

Things to Study Difference between an inside change and an outside change of a function – Inside Change affects the input(x) – Outside Change affects the output(y) Explaining Transformations – Through Graphs – Through Tables Quadratic Function – Vertex Form – Factor (Root) Form

Transforming Points Given the point (2,5) on the graph of f(x), give a point of each transformation. a)f(x-4) (6,5) b)f(x) – 4 (2,1) c)f(4x) (.5,5) d)4f(x) (2,20)

Complete the Table X f(x) f(-x) f(x)-2 f(x-2) 2f(x) f(x/2) f(3x)

Explain each Transformation from f(x) = 2 x a) f(-x) b) -f(-x)c) f(x) + 1.5d) 5f(x)

Write an Equation of the Quadratic Function Below y = 3(x-2) 2 or y = 3(x-2)(x-2)

Creating Equations If you know a quadratic function has a root at -1 and a vertex at (1,4), find an equation that would represent the function y = -1(x – 1) 2 + 4

Finding the Vertex Find the vertex of the following function. – Hint: Complete the Square… v(t) = t t - 4 Vertex: (-11/2, -137/4) (-5.5,-34.25)

Quadratic Problem A ball is thrown into the air. Its height (in feet) t seconds after the throw is given by: h(t) = 80t – 16t 2 a)Interpret h(2) Height after 2 seconds is 96 feet b)What is the ball maximum height traveled? (2.5, 100) 100 feet c)When will the ball hit the ground? (5, 0) 5 seconds

Explaining the Transformation