1. 5-38. Graph.
Warm Up
a. y = x2 + 6x = x2 + 6x = (x + 2)(x + 4) x + 2 = 0 or x + 4 = 0 x = -2 x = -4 (-2,0) (-4,0) = -3 2 y = (-3)2 + 6(-3) + 8 y = -1 (-3,-1)
b.    y = x2 + 6x
0 = x2 + 6x
0 = x(x + 6)
x = or x + 6 = 0
x = -6
(0,0) (-6,0)
= -3 2
y = (-3)2 + 6(-3)
y = -9
(-3,-9)

2. 5.1.4 Writing Equations for Quadratic Functions
HW: 5-43 through 5-48
5.1.4 Writing Equations for Quadratic Functions
January 20, 2016

3. Objectives
CO: SWBAT write a quadratic equation from a table by using the Zero Product Property in reverse.
LO: SWBAT explain how to use a table to create quadratic equations.

4. b = partners, rally table
5-39.  TABLE TO EQUATION You know how to make a table for a quadratic function, but how can you write an equation when given the table?  Write an equation for each table below.  What clues in the tables helped you determine the equations?  Verify your equations. b. a.
x = -3
x + 3 = 0
x = 2
x – 2 = 0
(x + 3)(x – 2) = 0
y = x2 + x - 6
x = -5
x + 5 = 0
x = 1
x – 1 = 0
(x + 5)(x – 1) = 0
y = x2 + 4x - 5
a = together
b = partners, rally table

5. 5-40.  Gwen is stuck while trying to write the equation for the quadratic function given in the following table.  Her teammate Sadie says “This looks like part (a) of the problem we just did, except the y-values are all doubled!  How can that help us?” Use Sadie’s observation to help you write the equation of the quadratic function given in the table below.
y = 2(x2 + x - 6)
y = 2x2 + 2x - 12
TEAM

6. 5-41.  WATER BALLOON CONTEST REVISITED Remember Imp’s water balloon launch?  Since the water balloon landed on the computer, you were given only a table of data, shown again below.  Write an equation that represents the height of Imp’s balloon as it traveled through the air.
x = 2
x – 2 = 0
(12,0) must be the other x-intercept by symmetry
x = 12
x – 12 = 0
(x – 2)(x – 12) = 0
y = x2 – 14x + 24
y = (3)2 – 14(3) + 24
y = -9
y = -(x2 – 14x + 24)
y = -x2 + 14x – 24
Together