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Daily Check #2. Factor the following quadratics... a) b) c). 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) = x 2 Today’s Question:

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slide1

Daily Check #2

Factor the following quadratics...

a)

b)

c)

questions over hw
Questions over hw?

He didn’t see the ewe turn!

math ii day 5 1 10 11
Math IIDay 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?
3 2 graphing quadratic functions in vertex or intercept form
3.2 Graphing Quadratic Functions in Vertex or Intercept Form
  • Definitions
  • 3 Forms
  • Graphing in vertex form
  • Examples
  • Changing between eqn. forms
quadratic function
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:

slide12

x – intercepts (-3,0) (1,0)

y – intercept (0,6)

vertex (-1,8)

Interval of Increase

Interval of Decrease

vertex
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 let s look at some parabolas scroll all the way down to the bottom examples
Example Websitelet’s look at some parabolasscroll all the way down to the bottom examples
  • Quadratics in Action
vertex form equation1
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
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
Now You Try.
  • Where is the vertex of
  • (x – 2)2 + 8
  • (x + 5)2 + 7
  • (x + 4)2 - 2

(2,8)

(-5,7)

(-4,-2)

vertex form
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
hold up wait a minute let s go back to that website and identify equations
Hold Up…..Wait a minutelet’s go back to that websiteand identify equations

http://www.analyzemath.com/quadraticg/quadraticg.htm

example graph y 5 x 3 2 4
Example: Graphy=-.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
Let’s do together
  • Analyze and Graph:

y = (x + 4)2 - 3.

(-4,-3)

now you try one
Now you try one!

y=2(x-1)2+3

  • Open up or down?
  • Vertex?
  • Axis of symmetry?
  • Table of values?
slide25

(-1, 11)

(3,11)

X = 1

(0,5)

(2,5)

(1,3)

classwork
Classwork

Page 67 #11 - 18

homework
Homework

Book Page 65 #13-18