Do you think Ms. Chavez can go through an small index card?

Do you think Ms. Chavez can go through an small index card?

Use Factoring to Solve Quadratic Application Problems

THE CIRCUS PHYSICSHTTP://VIDEO.PBS.ORG/VIDEO/1602463762/

1. What determines how high a juggling pin goes? 

2.What determines how far it travels horizontally while in the air?

3. How does change in the pin's vertical velocity compare to the change in horizontal velocity?

*Questions will be in Spanish for students

The Circus Physics

1. What determines how many objects a person can juggle?

2.  How does air resistance change things?

3.  Would juggling be the same on the Moon? How about Jupiter?

*Questions will be in Spanish for students

HOW DOES MATH PLAY INTO ALL THIS?

You can tell when an object will land on the ground by Factoring to solve Quadratic Equations.

The vertical motion of an object falling can be described by this formula:

h(t) = -16t^2 + (v)t + s

h: height of the object at any given moment. s: starting height of the object. t: the time in seconds. v: velocity of the object.

-16t^2: gravity *Note that gravity is negative, why do you think this is?

Juggler in Training  Suppose a juggler throws a pin into the air with an initial upward velocity of 29ft/s and an initial height of 6ft. The juggler isn't able to catch the pin. How long will it take the pin to hit the ground?

Lets plug in the information into our formula.

IF THE QUADRATIC EXPRESSIONSAX^2 + BX + C

CAN BE FACTORED, YOU CAN USE THE ZERO-PRODUCT PROPERTY

 TO SOLVE REAL-WORLD PROBLEMS.

You can also use Factoring to find the lengths of shapes.

A triangle has an area of 40cm^2 and the base of it is (2h+6). Find the height, h, of the triangle.

What's the triangle area formula?  A= 1/2bh

 Substitute the known values:40 = 1/2(2h+6)h40 = (h+3)h40 = h^2 + 3h0 = h^2 + 3h - 400 = (h + 8) (h - 5)

 h + 8 = 0             h - 5 = 0     h = -8                 h = 5 Which root doesn't make sense in the context of the problem?  The height of the triangle is 5cm.

X- Box Method

3 -9

Product

Sum

Factor the x-box wayExample: Factor 3x2 -13x -10

-13

(3)(-10)=

-30

-15 2

-10

-15x

2x

3x2

x -5

3x

+2

3x2 -13x -10 = (x-5)(3x+2)

Solving a Quadratic Equation by Factoring

Step 1: Write the equation in standard form.

Step 2: Factor completely.Step 3: Use the zero-factor property.

Set each factor with a variable equal to zero.

Step 4: Solve each equation produced in step 3.

Your Turn #1

A rectangular plot is 6 meters longer than it is wide. The area of the plot is 16 square meters.

Find the length and width of the plot using the area formula :   A= length x width sketch a picture

Your turn #2

A rock is thrown up from the cliff. Measured from the cliff's base, the height (in feet) of the rock after t seconds is given by the expression h(t) = -16t^2 + 64t + 80

a. sketch a drawing of the vertical motion. b. when will the rock hit the ground?

Your turn #3

A diver jumps from a diving board. The diver's height (measured in feet) at the time t is     h(t)= -16t^2 + 32t + 48 where t is the time in seconds h(t).

When will the diver hit the water? sketch a picture of the vertical motion.

Your turn #4

A first aid helicopter is dropping a package of medical supplies to the ground below. The function

h(t) = -16(t)^2 + 2t + 50

gives you the approximate height h(t) in feet above the ground the package is at (t) seconds after the package is dropped.

How many seconds pass from the time the package leaves the helicopter until the package hits the ground? Sketch a picture of the motion.

What are the Numbers?

The product of two consecutive negative integers is 1122. What are the numbers?

Remember that consecutive integers are one unit apart, so my numbers are n and n+1.

Factoring Puzzle

EXIT SLIPWrite or draw what you think the following words mean.•Factoring•Motion•Vertical Motion•Gravity

In your own words, write the steps for factoring quadratic equations.