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Ch 5 Pt 1 (5-1  5-3) Portfolio Page
-- Algebra 2
Lesson 5-1: Modeling Data with Quadratic Functions
--identify quadratic functions & their graph --Quadratic regression on graphing calculator
STANDARD
FORM OF QUADRATIC FUNCTION: y = ax2 + bx + c
Quadratic term: ax2 Linear term: bx Constant term: c
Example: Determine if the function is linear or quadratic. State the quadratic, linear, and constant terms:
GRAPH OF A QUADRATIC FUNCTION:
Parabola – the graph of a quadratic function
(U-shaped)
Axis of Symmetry -- the line that divides a
parabola into two parts that are mirror
images.
Vertex – the point at which the parabola
intersects the axis of symmetry.
If graph opens up, vertex is MINIMUM. If
graph opens down, vertex is MAXIMUM.
P
Q
Example:
1) State
2) State
3) State
4) State
vertex:
axis of symmetry:
P’
Q’
QUADRATIC REGRESSION ON GRAPHING CALCULATOR: Write a quadratic model given points on the graph.
In calculator:
Find the quadratic model for the values (1, 0), (2 , -3), (3, -10)
1) Turn Plots on/Turn Diagonistics ON (Catalog)
2) STAT / 1:Edit – enter x values in L1 and y values in L2
3) STAT / CALC / 5:QuadReg/ /Enter L , L
1
2
4) Y=/VARS/5:Statistics/EQ/1:RegEQ
The quadratic function is _____________________________
Example: The number of weekend get-away packages a hotel can sell can be modeled by
R = -0.12p2+ 60p, where p is the price of a get-away package and R is the hotel’s revenue. What
price will maximize the revenue? What is the maximum revenue? Predict the hotel’s revenue if the
cost of a get-away package is $100.
Lesson 5-2: Properties of Parabolas
--graphing from standard form --finding minimum and maximum values of quadratic functions
GRAPH FROM STANDARD FORM:
f(x) = ax2 + bx + c:
1)
2)
If a is (+), parabola opens up.
If a is (-), parabola opens down.
3)
Vertex: (
4)
5)
−𝒃
−𝒃
, 𝒇( ))
𝟐𝒂
𝟐𝒂
Axis of symmetry: x =
Y-intercept: (0, c)
−𝒃
𝟐𝒂
ALL GRAPHS SHOULD INCLUDE:
--axis of symmetry
--vertex
--two pts to left and right of vertex
Graph:
(y = ax2 + c)
Graph:
(y = ax2 + bx + c)
Lesson 5-3: Translating Parabolas
--Using Vertex Form to graph and write equations
VERTEX FORM OF QUADRATIC FUNCTION: y = a(x – h)2 + k
Vertex: (h, k)
Axis of Symmetry: x = h
Graph:
WRITING EQUATIONS: Given vertex and one point
Example:
IDENTIFY
VERTEX AND Y-INTERCEPT FOR EACH FUNCTION:
Example (standard form)
Example (vertex form)
STANDARD FORM/VERTEX FORM:
Convert the function to standard form:
Convert the function to vertex form: