Today’s Objective:Today’s Objective:PA Standard 2.8E,N,QPA Standard 2.8E,N,Q

Students will incorporate Students will incorporate the vertex of a quadratic the vertex of a quadratic

function for the purpose of function for the purpose of determining maximum determining maximum and minimum values.and minimum values.

Example: A basketball is shot from the free throw line from a height of six feet. What is the maximum height of the ball if the path of the ball is modeled by:

212 6.

9y x x

The path is a parabola opening downward. The maximum height occurs at the vertex.

2,9

1

ba

.92

92

91

2

2

2

a

bx

15618)81(9

19

2

fa

bf

So, the vertex is (9, 15). The maximum height of the ball is 15 feet.

What does ‘9’ represent: Distance of the ball from the free throw line when it reaches its maximum height.

Example: The amount of revenue, R, in dollars, realized by a company in terms of the number of appliances produced, x , is shown by :

Find the number of appliances produced which provides the maximum revenue and then find the maximum revenue.

900,1.0 ba

4500)1.0(2

900

2

a

bx

000,025,2)4500(1.0)4500(90045002

2

fa

bf

So, the vertex is (4500, 2025000)).

The company can realize maximum revenue of $2,025,000 by producing 4500 appliances.

21.0900 xxR

4500 appliances produced will provide the maximum revenue

Example: A manufacturer has daily production costs of :

where ‘C’ is the total cost, in dollars, and ‘x’ is the number of computer games produced. Find the number of computer games which should be produced each day to yield a minimum cost.

120,055.0 ba

1091)055.0(2

120

2

a

bx

We just need the x-coordinate to solve the problem so:

The company can realize a minimum cost by producing 1091 computer games.

2055.0120000,20 xxC

The graph is a parabola opening upward. The minimum values occurs at the vertex.

AssignmentAssignmentPP. 244 – 245:PP. 244 – 245:

28 – 30, 37-39, 5428 – 30, 37-39, 54