Daily Check #2
Factor the following quadratics...
a)
2x  7 x  3
2
b) 3x  11x  6
2
c) 4x  28x  49
2
Questions over hw?
He didn’t see the ewe turn!
Math II
Day 5 (1-10-11)
Standard MM2A3
•
b – Graph quadratic functions as
transformations of the function f(x) = x2
Today’s Question:
How to we graph a parabola using
vertex form?
Intro to Parabolas
Dude Perfect Video
3.2 Graphing Quadratic Functions
in Vertex or Intercept Form
• Definitions
• 3 Forms
• Graphing in vertex form
• Examples
• Changing between eqn. forms
Quadratic Function
• A function of the form y=ax2+bx+c
where a≠0 making a u-shaped graph
called a parabola.
Example quadratic equation:
x – intercepts (-3,0) (1,0)
y – intercept (0,6)
vertex (-1,8)
Interval of Increase
Interval of Decrease
Vertex• The lowest or highest point
of a parabola.
Vertex
Axis of symmetry• The vertical line through the vertex of the
parabola.
Axis of
Symmetry
Example Website
• Quadratics in Action
let’s look at some parabolas
scroll all the way down to the
bottom examples
The 3 Forms of Quadratics
Factored
Vertex Form
Standard
Form
(x+4)(x-9)
(x-2.5)2 - 42.25
x2-5x-36
Vertex Form Equation
2
y=a(x-h) +k
Vertex Form Equation
y=a(x-h)2+k
• If a is positive, parabola opens up
If a is negative, parabola opens down.
• The vertex is the point (h,k).
• If a > 1 the parabola gets skinny
• If a < 1 the parabola gets fatter
• The vertex is the point (h,k).
• The axis of symmetry is the vertical line
x=h.
Tip for the Vertex
• (x – h)2 + k
• The y doesn’t lie
• But the x does – we must change its
sign.
• (x – 3)2 + 7
– Vertex will be at (3,7)
Now You Try.
• Where is the vertex of
• (x – 2)2 + 8
(2,8)
• (x + 5)2 + 7
(-5,7)
• (x + 4)2 - 2
(-4,-2)
Vertex Form
Each function we just looked at can be written in the
form (x – h)2 + k, where (h , k) is the vertex of the
parabola, and x = h is its axis of symmetry.
(x – h)2 + k – vertex form
Equation
Vertex
Axis of Symmetry
y = x2 or
y = (x – 0)2 + 0
(0 , 0)
x=0
y = x2 + 2 or
y = (x – 0)2 + 2
(0 , 2)
x=0
y = (x – 3)2 or
y = (x – 3)2 + 0
(3 , 0)
x=3
Hold Up…..Wait a minute
let’s go back to that website
and identify equations
http://www.analyzemath.com/quadraticg/quadraticg.htm
Example: Graph
y=-.5(x+3)2+4
•
•
•
•
a is negative (a = -.5), so parabola opens down.
Vertex is (h,k) or (-3,4)
Axis of symmetry is the vertical line x = -3
Table of values
x -.5(x+3)2+4 y (x, y)
Vertex (-3,4)
-1
-.5(-1+3)2+4
2 (-1,2)
-2
-.5(-2+3)2+4
2
(-2,3.5)
-4
-.5(-4+3)2+4
2
(-3,3.5)
-5
-.5(-5+3)2+4
2 (-4,2)
(-4,3.5)
(-2,3.5)
(-5,2)
(-1,2)
x=-3
Let’s do together
• Analyze and Graph:
y = (x + 4)2 - 3.
(-4,-3)
Now you try one!
y=2(x-1)2+3
• Open up or down?
• Vertex?
• Axis of symmetry?
• Table of values?
(-1, 11)
(3,11)
X=1
(0,5)
(2,5)
(1,3)
Classwork
Page 67 #11 - 18
Homework
Book Page 65 #13-18