Section 9 – 2 Quadratic Functions

Objective: To graph quadratic functions of the

form cbxaxy 2

𝑦=𝑎𝑥2+𝑏𝑥+𝑐The b affects the position of the axis of

symmetry, which also changes the position of the vertex.

𝑦=𝑎𝑥2+𝑏𝑥+𝑐The equation of the axis of symmetry is related to the ratio of

Axis of SymmetryThe Equation of the Axis of Symmetry is:

The x-coordinate of the vertex is also

Problem #1 Graphing A) What is the graph of the function ?

Problem #1 Graphing B) What is the graph of the function ?

Problem #1 Graphing C) What is the graph of the function ?

What is the graph of the function ?

Problem #1Got It?

HOMEWORKTextbook Page 556-557;

#8 – 14 Even#16 – 19 All

#20 – 24 Even

Section 9 – 2 Continued…

Objective: To examine practical applications of

quadratic functions.

h

This formula can be used to determine the approximate height

above the ground of an object projected in the air, given an initial upward velocity continues with no

additional force acting on it.

Problem #2 Using the Vertical Motion Model

A) During halftime of a basketball game, a slingshot, that is 5 feet above the ground, launches t-shirts at the crowd. A t-shirt is launched with an initial upward velocity of 72 ft/s. The t-shirt is caught 35 feet above the court. How long will it take the t-shirt to reach its maximum height? What is its maximum height? What is the range of the function that models the height of the t-shirt over time?

Problem #2 Using the Vertical Motion Model

B) Daniel kicks a soccer ball up into the air with an initial upward velocity of 64 feet per second. The ball is 2 feet above the ground when it is kicked. How long will it take the ball to reach its maximum height? How high above the ground will it be? What is the range of the function?

Problem #2 Using the Vertical Motion Model

C) A punter kicked the football into the air with an upward velocity of 62 ft/s. Its height in feet after t seconds is given by the formula . What is the maximum height the ball reaches? How long will it take the football to reach the maximum height? How long does it take for the ball it hit the ground?

HOMEWORKTextbook Page 557;

#26, 27