Transcript 2.1.4 transforming parabola notes

2.1.4 Quadratic Function Family
Essential Question:
How do you transform parabolas using various
forms and the function family?
Main Idea
• In Algebra I, you learned about the standard
form of a quadratic equation in order to write,
solve, and graph parabolas.
• We are going to learn about another form to
support your understanding of parent functions
and transformations.
– What is standard form?
– What are parent functions?
– What are the basic transformations?
Quadratic Functions
Forms
• Standard form:
– f(x) = ax2 + bx + c
• Where a,b,c are real
numbers
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Used to write and solve
Not quick to graph
a stretches or shrinks
c is the y-intercept
• Vertex form:
– f(x) = a(x – h)2 + k
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a (stretch or shrink)
h (horizontal shift)
k (vertical shift)
(h,k) = vertex
• Use to write and solve
• Quicker to graph with
vertex
• Transformations change
from parent function
Vertex Form to Graph
• Summarize the steps and discuss how this varies from
graphing standard form.
Vertex Form to Graph
To Graph with Vertex form:
1) Use (h,k) to plot the vertex and h to plot the
axis of symmetry
2) Find another point and mirror it
3) Connect with a curve
Graph with Vertex Form
Vertex Form from a Graph
• Summarize the steps and discuss.
Writing in Vertex Form
• To find the equation from a graph:
1) Find the vertex for h and k
2) Identify another point for x and y
3) Plug in (h,k) and (x,y) to vertex form
4) Solve for a
5) Write the equation in vertex form with a, h, k
Practice
Forms in Comparison
Prediction
• Considering the two forms, how can you
change from one to the other?
– What other function have you done this with?
Why were those forms important? What are they?
Converting to Vertex Form
• Summarize the steps and discuss.
Standard to Vertex
• Standard form to Vertex form:
1)
2)
3)
4)
Find the axis of symmetry (x=-b/2a)
Plug in x to find y for the vertex
Use the vertex for h and k
Use the original a value
Practice
Practice
Prediction
• How can we convert vertex form to standard
form? Why?
Vertex to Standard
• Vertex form to Standard form:
1) Multiply (x-h)2
2) Distribute a to the parentheses
3) Combine like terms to include k
4) Write in order
Practice
1) y = 3(x+6)2 – 1
2) y = -1/2(x-2)2+3
Summary
• Write a paragraph, with detailed, complete
sentences.
• How do you transform parabolas using
various forms and the function family?
• Write 3-5 study questions in the left column
to correspond with the notes.