SLIDE 1
DAY 123 – DOMAIN AND RANGE OF
A QUADRATIC FUNCTION
EXAMPLE1
Suppose a defender is 3 yards in front of the receiver. This means the defender is 37 yards from the
- quarterback. Will he able to deflect or catch the ball?
E XAMPLE 1 Suppose a defender is 3 yards in front of the receiver. - - PowerPoint PPT Presentation
E XAMPLE 1 Suppose a defender is 3 yards in front of the receiver. - - PowerPoint PPT Presentation
D AY 123 D OMAIN AND RANGE OF A QUADRATIC FUNCTION E XAMPLE 1 Suppose a defender is 3 yards in front of the receiver. This means the defender is 37 yards from the quarterback. Will he able to deflect or catch the ball? S OLUTION The answer
SLIDE 2
SLIDE 3
SOLUTION
The answer depends on how high the ball is when it reaches him. The height is represented by h in the above
- equation. Substitute 37 for x in the equation.
The ball will be 8.775 feet above the ground when it reaches the defender. Since 0.775 * 12 inches ≈ 9 inches, this is approximately 8 feet 9 inches. To deflect or intercept the ball, the defender would have to reach a height of 8 feet 9
- inches. With a well-timed jump, this is possible for most
defenders.
775 . 8 6 37 225 . 34 6 37 1369 025 . 6 37 37 025 . 6 025 .
2 2
x x h
SLIDE 4
EXAMPLE2
Because of the coefficients in the equations, we recommend that students use automatic graphers. If students do not have graphers, we recommend that you either provide a partial table of values or allow more time for this work.
SLIDE 5
EXAMPLE2
A model rocket is shot at an angle into the air from the launch pad.
- 1. The height of the rocket when it has traveled
horizontally x feet from the launch pad is given by
- a. Graph this equation
x x h 43 . 11 163 .
2
SLIDE 6
EXAMPLE2
A model rocket is shot at an angle into the air from the launch pad.
- 1. The height of the rocket when it has traveled
horizontally x feet from the launch pad is given by
- a. Graph this equation
x x h 43 . 11 163 .
2
SLIDE 7
EXAMPLE2
- b. A 75-foot tree, 10 feet from the launch pad, is in the
path of the rocket. Will the rocket clear the top of the tree?
- c. Estimate the maximum height that the rocket will
reach.
SLIDE 8
EXAMPLE2 - ANSWER
- b. A 75-foot tree, 10 feet from the launch pad, is in the
path of the rocket. Will the rocket clear the top of the tree? Yes; at 10 feet from the launch pad, the rocket is 98 feet high
- c. Estimate the maximum height that the rocket will
reach. About 200 feet
SLIDE 9
EXAMPLE3
The equation gives the height h in feet of another ball t seconds after being thrown from a height of 6 feet with an initial upward velocity of 32 feet per second.
- a. How high will the ball be a half second
after it is thrown?
- b. What is the maximum height this ball
reaches?
6 32 16 2 t t h
SLIDE 10
EXAMPLE3 - ANSWER
- a. Substitute 0.5 for t in
- b. In half a second, the ball will be 18 feet