Matching Puzzle

Grab a pair of scissors, a puzzle sheet and sit at your

desk.

Warm up: Write the WHOLE problem down.

1. The data below represents the height of a rocket shot from 150 ft above ground and traveling at a velocity of 50 m/second. Find the quadratic equation that models this data.

2. What form of the quadratic equation did we get from this data?

Seconds 0 1 2 3 4 5Meters 150 195.1 230.44 255.9 271.6 277.5

Answer:

• We can look at this equation and determine a few things about the Projectile Motion Function.

• x=time• y=height• a= downward acceleration due to gravity:

-4.9 m/ or -16 ft/• = initial upward velocity• =initial height in meters or feet.

Follow up

• Now find the maximum height reached by the rocket, and how many seconds it took to get there.

• In order to answer this question we need to know the______?

• Can we determine the vertex given the general equation?

• What form to we need?

Goal

• To convert a quadratic equation from General Form to Vertex Form.

• Method: Completing the Square.

Factoring: Completing the Square

General to Vertex form

• We want to go from

To

Completing the Square Method

The two relationships that will allow us to make this conversion are:and

Example 1

• Write in vertex form.

• Step 1: identify a,b and c.• a=1, b=-10, c=15

Cont…

• Step 2: substitute values into the relations

Cont…

• Step 3: Substitute the values for h and k into the vertex form.

• Vertex form:

• h=5, k=-10, a=1 (never changed)

• Solution:

Example 2

• Factor • a=_____, b=______, c=_______

Find h and k.• Plug h and k into • Answer:

State the vertex

• What is the vertex of the previous problem?

• Answer: (-5,0)

Example 3: You try

• What is the vertex of ?

Example 4: You try again

• Write the following equation in vertex form.

Example 5

• Write the following equation in vertex form.

• Hint: first convert factored form to general form, the change to vertex form)

Example 6

• Find the vertex:

Homework

• 7.3: Skip #2• This is a big assignment. Pace yourself!• The only way to really understand this stuff is

to Practice…A LOT!