Parabolas And Quadratic Worksheet
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1
2C
5 P
1 P
P
– 5-1
5-5
H
T
ORTFOLIO
AGE
THROUGH
Lesson 5-1: Modeling Data with Quadratic Functions
--identify quadratic functions & their graph --Quadratic regression on graphing calculator
S
Q
F
: y = ax
+ bx + c
2
TANDARD FORM OF
UADRATIC
UNCTION
Quadratic term: ax
Linear term: bx Constant term: c
2
Example: Determine if the function is linear or quadratic. State the quadratic, linear, and constant terms:
1) f(x) = 3x
– (x + 3)(2x – 1)
2
f(x) = x
– 5x + 3; quadratic/ x
/ -5x / 3
2
2
G
Q
F
:
RAPH OF A
UADRATIC
UNCTION
(4, 1)
Parabola – the graph of a quadratic function
Example:
(U-shaped)
X = 4
1) State vertex:
P
Axis of Symmetry -- the line that divides a
2) State axis of symmetry:
parabola into two parts that are mirror
(2, 0)
3) State P’
images.
4) State Q’
Vertex – the point at which the parabola
(8, -3)
Q
intersects the axis of symmetry.
If graph opens up, vertex is MINIMUM. If
graph opens down, vertex is MAXIMUM.
Q
R
G
C
: Write a quadratic model given points on the graph.
UADRATIC
EGRESSION ON
RAPHING
ALCULATOR
In calculator:
1) STAT / 1:Edit – enter x values in L1 and y values in L2
2) STAT / CALC / 5:QuadReg
3) VARS / Y-VARS / 1:Function / 1:Y1
4) ENTER
Substitute values of a, b, and c into standard form.
Example: Find the quadratic model for the values (-1, 10), (2, 4), (3, -6)
Y = -2x
+ 12
2
The quadratic function in standard form is ____________________________________
Lesson 5-2: Properties of Parabolas
--graphing from standard form --finding minimum and maximum values of quadratic functions
Graph:
(y = ax
+ c)
2
G
S
F
:
Graph:
(y = ax
+ bx + c)
2
RAPH FROM
TANDARD
ORM
Ex: y = -x
+ 4
2
Ex: y = x
+ 2x - 6
2
f(x) = ax
+ bx + c:
2
V: (0, 4)
V: (-1, -7))
1)
If a is (+), parabola opens up.
Pts: (1, 3);(2, 0)
2)
If a is (-), parabola opens down.
Pts: (0, -6);(1, -3)
−��
−��
3)
Vertex: (
, ��(
))
����
����
−��
4)
Axis of symmetry: x =
����
5)
Y-intercept: (0, c)
A
:
LL GRAPHS SHOULD INCLUDE
--axis of symmetry
--vertex
--two pts to left and right of vertex
M. M
URRAY
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