Use Factoring to Solve Quadratic Word Problems

ax^2 + bx + c

The Circus Physicshttp://video.pbs.org/video/1602463762/

What determines how high a juggling pin goes? What determines how far it travels horizontally while in the air? How does change in the pin's vertical velocity compare to the change in horizontal velocity?

If you throw a ball into the air, what will it's path look like?   As a ball moves horizontally, gravity pulls down on it. Physicists call this projectile motion.

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?

How does math play into all this?

Using factoring, you can tell when an object will land on the ground.

Oops... My bad!  

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

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

h = -16t^2 + (v)t + sh: height of the object at any given moment. s: starting height of the object. t: the time in seconds. v: velocity of the object. *note that gravity is negative because it is acting in an opposite direction to the initial velocity.:

If the quadratic expressionsax^2 + bx + c

can be factored, you can use the Zero-Product Property

 to solve Real-World Problems.

The triangle shown below has an area of 40cm^2. 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.

Your Turn #1

Suppose you throw a ball in the air. The ball is 6 ft high when it leaves your hand. Use the quadratic equation 0= -16t^2 + 20t + 6to find the number of seconds t that the ball is in the air.

The vertical motion of an object falling can be described by this formula:   h = -16t^2 + (v)t + s sketch a picture of the vertical motion.

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 verticle 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

After the semester is over, you discover that Aurora University will not buy back your geometry. You got to the roof of a 12-story building and look over the edge to the pool 160ft below. You chuck your book 48 feet per seconds. Use the expressionh(t) = -16^2-48t+160

After how many seconds did the book hit the water? Sketch a picture of the vertical motion

Your turn #5

Your cell phone is upstairs in your room and it starts to ring. Your little sister throws it down to you from the balcony. You suck at catching.  Use the expression 

t^2 - 4t + 21

When does your phone hit the ground? Sketch a picture of the vertical motion.

Huh???

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.