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 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.     2 h 0 . 025 x x 6      2 0 . 025 37 37 6      0 . 025 1369 37 6     34 . 225 37 6  8 . 775 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.

E XAMPLE 2 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.

E XAMPLE 2 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 2    . 163 11 . 43 h x x a. Graph this equation

E XAMPLE 2 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 2    . 163 11 . 43 h x x a. Graph this equation

E XAMPLE 2 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.

E XAMPLE 2 - A NSWER 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

E XAMPLE 3     The equation gives the 16 2 h t 32 t 6 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?

E XAMPLE 3 - A NSWER     a. Substitute 0.5 for t in 16 2 h t 32 t 6 .     2 h 16 (. 5 ) 32 (. 5 ) 6     16 (. 25 ) 16 6    4 22  18 b. In half a second, the ball will be 18 feet high