Daily Check #2 Factor the following quadratics... a) b) c)

Daily Check #2Factor the following quadratics...

a)

b)

c)

22 7 3x x

23 11 6x x

24 28 49x x

Questions over hw?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?

Intro to Parabolas

Dude Perfect Video

3.2 Graphing Quadratic 3.2 Graphing Quadratic FunctionsFunctions in Vertex or in Vertex or

Intercept FormIntercept Form

• DefinitionsDefinitions

• 3 Forms3 Forms

• Graphing in vertex formGraphing in vertex form

• ExamplesExamples

• Changing between eqn. formsChanging between eqn. forms

Quadratic FunctionQuadratic Function•A function of the form A function of the form

y=axy=ax22+bx+c where a+bx+c where a≠0 making a ≠0 making a u-shaped graph called a u-shaped graph called a parabolaparabola..

Example quadratic equation:

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 pointThe lowest or highest point

of a parabola.of a parabola.

VertexVertex

Axis of symmetry-Axis of symmetry-

• The vertical line through the vertex of the The vertical line through the vertex of the parabola.parabola.

Axis ofSymmetry

Example WebsiteExample Website

let’s look at some parabolaslet’s look at some parabolas

scroll all the way down to scroll all the way down to the bottom examplesthe bottom examples

•Quadratics in Action

The 3 Forms of QuadraticsThe 3 Forms of Quadratics

Factored Vertex FormStandard

Form

(x+4)(x-9) (x-2.5)2 - 42.25 x2-5x-36

Vertex Form EquationVertex Form Equation

y=a(x-h)y=a(x-h)22+k+k

Vertex Form EquationVertex Form Equationy=a(x-h)y=a(x-h)22+k+k

• If a is positive, parabola opens upIf a is positive, parabola opens up

If a is negative, parabola opens down.If a is negative, parabola opens down.

• The vertex is the point (h,k).The vertex is the point (h,k).

• If a > 1 the parabola gets skinnyIf a > 1 the parabola gets skinny

• If a < 1 the parabola gets fatterIf a < 1 the parabola gets fatter

• The vertex is the point (h,k).The vertex is the point (h,k).

• The axis of symmetry is the vertical line The axis of symmetry is the vertical line x=h.x=h.

Tip for the VertexTip for the Vertex

• (x – h)(x – h)22 + k + k

• The The yy doesn’t lie doesn’t lie

• But the But the xx does – we must change does – we must change its sign.its sign.

• (x – 3)(x – 3)22 + 7 + 7– Vertex will be at (3,7)Vertex will be at (3,7)

Now You Try.Now You Try.

• Where is the vertex of Where is the vertex of

• (x – 2)(x – 2)22 + 8 + 8

• (x + 5)(x + 5)22 + 7 + 7

• (x + 4)(x + 4)22 - 2 - 2

(2,8)

(-5,7)

(-4,-2)

Vertex FormVertex FormEach function we just looked at can be written Each function we just looked at can be written

in the form (x – h)in the form (x – h)22 + k, where (h , k) is the + k, where (h , k) is the vertex of the parabola, and x = h is its axis of vertex of the parabola, and x = h is its axis of symmetry.symmetry.

(x – h)(x – h)22 + k – vertex form + k – vertex formEquationEquation VertexVertex Axis of Axis of

SymmetrySymmetry

y = xy = x22 or or y = (x – y = (x – 00))22 + + 00

((00 , , 00)) x = x = 00

y = xy = x22 + 2 or + 2 ory = (x – y = (x – 00))22 + + 22

((0 0 , , 22)) x = x = 00

y = (x – y = (x – 33))22 or or y = (x – y = (x – 33))22 + + 00

((33 , , 00)) x = x = 33

Hold Up…..Wait a minuteHold Up…..Wait a minutelet’s go back to that websitelet’s go back to that website

and identify equationsand identify equations

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

Example: GraphExample: Graphy=-.5(x+3)y=-.5(x+3)22+4+4• a is negative (a = -.5), so parabola opens down.a is negative (a = -.5), so parabola opens down.• Vertex is (h,k) or (-3,4)Vertex is (h,k) or (-3,4)• Axis of symmetry is the vertical line x = -3Axis of symmetry is the vertical line x = -3• Table of valuesTable of values

x x -.5(x+3)-.5(x+3)22+4 +4 y (x, y) y (x, y)Vertex (-3,4)

(-4,3.5)

(-5,2)

(-2,3.5)

(-1,2)

x=-3

-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)

Let’s do togetherLet’s do together

•Analyze and Graph:Analyze and Graph:

y = (x + 4)y = (x + 4)22 - 3. - 3.

(-4,-3)

Now you try one!Now you try one!

y=2(x-1)y=2(x-1)22+3+3

•Open up or down?Open up or down?

•Vertex?Vertex?

•Axis of symmetry?Axis of symmetry?

•Table of values?Table of values?

(-1, 11)

(0,5)

(1,3)

(2,5)

(3,11)

X = 1

ClassworkClasswork

Page 67 #11 - 18

HomeworkHomework

Book Page 65 #13-18