Ch 6 - GraphingDay 1 - Section 6.1

Quadratics and Absolute Values

parent function: y = x2

y = a(x - h)2 + k

vertex (h, k)

a describes the steepness

graph is a parabola (u-shaped)

parent function: y = |x|

y = a|x - h| + k

vertex (h, k)

a describes the steepness

graph is a v-shape

Stretching, Shrinking, and

Reflectingthese properties work with all graph

our notes will focus on quadratic and absolute value graphs

Vertical Stretching

when a > 1

function notation: y = a[f(x)]

verbally: the function is stretched vertically by a factor of a

Vertical Shrinking

when 0 < a < 1

function notation: y = a[f(x)]

verbally: the function is shrunk vertically by a factor of a

Vertical Reflection

when a < 0

function notation: y = -[f(x)]

verbally: the function is reflected over they x-axis

But what happens if the input is multiplied?

Let h(x) be represented by the table below.

Graph h(x), 2h(x), and h(2x)

x -2 -1 0 1 2y 1 -2 1 -2 1

Horizontal Shrinking

when b > 1

function notation: y = f(bx)

verbally: the function is horizontally shrunk by a factor of 1/b.

Horizontal Stretching

when 0 < b < 1

function notation: y = f(bx)

verbally: the function is horizontally stretched by a factor of 1/b.

SummaryVertical Dilations - when the output is multiplied by a constant

Reflection over the x-axis when the output is made negative

Horizontal Dilations - when the input is multiplied by a constant

Reflection over the y-axis when the input is made negative

Describe how the parent function, p(x) is

transformed to h(x)

1. p(x) = x3 and h(x) = -2x3

2. p(x) = x3 + 1 and h(x) = (4x)3 + 1

3. p(x) = 3x - 2 and h(x) = 15x - 10

Sketch the graph given the transformations.

1.shrunk vertically by a factor of 2

2.y = -f(x)3.g(x) = f(x/3)