module 19.2 transforming quadratic functions · 2018-04-04 · in module 19.1 we mentioned standard...
TRANSCRIPT
Module 19.2
Transforming Quadratic Functions
P. 903
How can you obtain the graph of 𝒈 𝒙 = 𝒂(𝒙 − 𝒉)𝟐+𝒌from the graph of 𝒇 𝒙 = 𝒙𝟐?
P. 904
We know what 𝑓 𝑥 = 𝑥2 looks like. But what does the function look like when it is shifted up or down?
P. 906
We know what 𝑓 𝑥 = 𝑥2 looks like. But what does the function look like when it is shifted left or right?
P. 908
Quadratic functions can take three forms – Standard, Vertex, and Factored.In Module 19.1 we mentioned Standard Form: 𝒇 𝒙 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄Here’s Vertex Form:
𝒈 𝒙 = 𝒂(𝒙 − 𝒉)𝟐 + 𝒌
Width Horizontal Translation
Vertical Translation
Sign
The point (h,k) is the vertex.The Axis of Symmetry runs through 𝒉.So the equation for that line is 𝒙 = 𝒉.
Example: 𝒈 𝒙 = 𝟑(𝒙 − 𝟐)𝟐 + 𝟒In this case, the vertex (h,k) = (2,4).Example: 𝒈 𝒙 = −𝟑 𝒙 + 𝟏 𝟐 − 𝟑In this case, the vertex (h,k) = (–1, –3).
To graph a function in this form:
1) Identify the vertex.2) Generate two points on either side of the vertex.3) Draw the parabola!
P. 908
Helpful: Determine from a whether the parabola should open upward or downward. Does it match your graph?