Daily Check

1. Factor: 3x2 + 10x + 8

2. Factor and Solve: 2x2 - 7x + 3 = 0

Math I

UNIT QUESTION: What is a quadratic function?Standard: MM2A3, MM2A4

Today’s Question:How do you graph quadratic functions in vertex form?Standard: MM2A3.b.

3.2 Graphing Quadratic Functions in Vertex or Intercept

Form

• Definitions• 3 Forms

• Steps for graphing each 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:

Vertex-

• The lowest or highest pointof a parabola.

Vertex

Axis of symmetry-

• The vertical line through the vertex of the parabola.

Axis ofSymmetry

Vertex Form Equationy=a(x-h)2+k

• If a is positive, parabola opens upIf a is negative, parabola opens down.

• The vertex is the point (h,k).• The axis of symmetry is the vertical

line x=h.• Don’t forget about 2 points on either

side of the vertex! (5 points total!)

Vertex FormEach 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 formEquation Vertex Axis of

Symmetry

y = x2 or y = (x – 0)2 + 0

(0 , 0) x = 0

y = x2 + 2 ory = (x – 0)2 + 2

(0 , 2) x = 0

y = (x – 3)2 or y = (x – 3)2 + 0

(3 , 0) x = 3

Example 1: Graph y = (x + 2)2 + 1• Analyze y = (x + 2)2 + 1.• Step 1 Plot the vertex (-2 , 1)• Step 2 Draw the axis of symmetry, x = -

2.• Step 3 Find and plot two points on one

side , such as (-1, 2) and (0 , 5).

• Step 4 Use symmetry to complete the graph, or find two points on the

• left side of the vertex.

Your Turn!• Analyze and Graph: y = (x + 4)2 - 3.

(-4,-3)

Example 2: 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 y

-1 2 -2 3.5

-3 4 -4 3.5 -5 2

Vertex (-3,4)

(-4,3.5)

(-5,2)

(-2,3.5)

(-1,2)

x=-3

Now you try one!

y=2(x-1)2+3

• Open up or down?• Vertex?

• Axis of symmetry?• Table of values with 4 points

(other than the vertex?

(-1, 11)

(0,5)

(1,3)

(2,5)

(3,11)

X = 1

Intercept Form Equationy=a(x-p)(x-q)

• The x-intercepts are the points (p,0) and (q,0).

• The axis of symmetry is the vertical line x=

• The x-coordinate of the vertex is• To find the y-coordinate of the vertex, plug

the x-coord. into the equation and solve for y.

• If a is positive, parabola opens upIf a is negative, parabola opens down.

2

qp 2

qp

Example 3: Graph y=-(x+2)(x-4)• Since a is negative,

parabola opens down.

• The x-intercepts are (-2,0) and (4,0)

• To find the x-coord. of the vertex, use

• To find the y-coord., plug 1 in for x.

• Vertex (1,9)

2

qp

12

2

2

42

x

9)3)(3()41)(21( y

• The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex)

x=1

(-2,0) (4,0)

(1,9)

Now you try one!

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

• Open up or down?• X-intercepts?

• Vertex?• Axis of symmetry?

(-1,0) (3,0)

(1,-8)

x=1

Changing from vertex or intercepts form to standard

form• The key is to FOIL! (first, outside,

inside, last)• Ex: y=-(x+4)(x-9) Ex: y=3(x-

1)2+8 =-(x2-9x+4x-36) =3(x-1)(x-

1)+8 =-(x2-5x-36) =3(x2-x-

x+1)+8y=-x2+5x+36 =3(x2-

2x+1)+8 =3x2-

6x+3+8 y=3x2-6x+11

Challenge Problem

• Write the equation of the graph in vertex form.

23( 2) 4y x

AssignmentDay 1 -p. 65

#4,6,7,9,13,16

and Review for Quiz

Day 2 – p. 67 #4,5,7,9,11-14

We will not do intercept form.