Daily Check #2

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# Daily Check #2 - PowerPoint PPT Presentation

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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## Daily Check #2

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Daily Check #2

a)

b)

c)

Questions over hw?

He didn’t see the ewe turn!

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
• Definitions
• 3 Forms
• Graphing in vertex form
• Examples
• Changing between eqn. forms
• A function of the form y=ax2+bx+c where a≠0 making a u-shaped graph called a parabola.

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 Websitelet’s look at some parabolasscroll all the way down to the bottom examples
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
• (x + 5)2 + 7
• (x + 4)2 - 2

(2,8)

(-5,7)

(-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
Hold Up…..Wait a minutelet’s go back to that websiteand identify equations

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
• 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