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 TableX -3 -2 -1 0 1 2 3

f(x) -4 -1 2 3 0 -3 -6

f(-x)

f(x)-2

f(x-2)

2f(x)

f(x/2)

f(3x)

Explain each Transformation from f(x) = 2x

a) f(-x) b) -f(-x) c) f(x) + 1.5 d) 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) = t2 + 11t - 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 – 16t2

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