Ch 6 - Graphing Day 1 - Section 6.1. Quadratics and Absolute Values parent function: y = x 2 y = a(x...
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Transcript of Ch 6 - Graphing Day 1 - Section 6.1. Quadratics and Absolute Values parent function: y = x 2 y = a(x...
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)