Mastering Quadratic Functions: Graphing Through Transformations
Graphing Quadratics
4.2 Vertex Form
Vertex form
•
vertex form
: where (h, k) is the vertex
•
Parent graph of y = x^2
Transformation rules for quadratic
•
Parent
:
•
moves
left or right
the opposite of the sign
•
moves
up or down
with the sign
•
vertical stretch
if a > 1,
vertical shrink
if 0< a < 1
•
reflects
across the x-axis (turns up-side-down)
Steps for Graphing quadratics through
transformations
•
Find the vertex this is (h, k) remember h is opposite sign
•
Plot the vertex
•
Create a table to graph four more points two on each side of the
vertex
•
Column 1 labeled x
•
Column 2 labeled f(x)
•
Plug the numbers into the equation
•
Using the numbers from the table to plot your other four points
•
Draw in your U shape
Example
Example
Example
Example
You Try
Homework
•
Worksheet
•
1-12 (Do a, b, c, and d for all problems)
Explore the vertex form of quadratic equations, understand transformation rules, and learn step-by-step methods for graphing quadratics with examples and practice problems. Enhance your skills in identifying vertices, plotting points, and visualizing the U-shaped graphs of quadratic functions.
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Presentation Transcript
Graphing Quadratics 4.2 Vertex Form
Vertex form vertex form: where (h, k) is the vertex Parent graph of y = x^2
Transformation rules for quadratic Parent : moves left or right the opposite of the sign moves up or down with the sign vertical stretch if a > 1, vertical shrink if 0< a < 1 reflects across the x-axis (turns up-side-down)
Steps for Graphing quadratics through transformations Find the vertex this is (h, k) remember h is opposite sign Plot the vertex Create a table to graph four more points two on each side of the vertex Column 1 labeled x Column 2 labeled f(x) Plug the numbers into the equation Using the numbers from the table to plot your other four points Draw in your U shape
Homework Worksheet 1-12 (Do a, b, c, and d for all problems)
