Evaluating and Solving Quadratic Functions Duffer McGee stood on a hill and used a nine iron to hit a golf ball that reached a maximum height of 169 feet and stayed in the air for 6.1 seconds before it touched the ground. Pretty good for a Duffer. Neptune has a gravity of approximately 36 feet per second squared compared to Earth's 32 feet per second squared. NASA did a simulation to try to determine how high the golf ball would fly and how long it would stay in the air on Neptune if it was hit at the same height, angle and velocity as Duffer's. The data below represent the results of that simulation: t 1 2 3 4 5 H(t) 114 150 150 114 42 Use the Quadratic Regression feature of your calculator to generate a mathematical model for this situation. Write the function below. Round each coefficient to the nearest whole number. H(t) Based on your model how high is the hill from which the golf ball was hit?? feet high. The golf ball was hit from a hill Use your model to estimate how long the golf ball will take to reach its maximum height and what its maximum height will be. Round your answers to two decimal places. The golf ball will reach a maximum height of seconds. feet after Use your model to determine how long it will take for the golf ball to hit the surface of Neptune. Round your answer to two decimal places. The golf ball will reach the surface of Neptune after seconds.

A ball is thrown upward and outward from a height of 6 feet. The height of the ball, f(x), in feet, can be modeled by f(x) = -0.8x2 + 3.2x + 6, where x is the ball’s horizontal distance, in feet, from where it was thrown. Solve; a. What is the maximum height of the ball and how far from where it was thrown does this occur? b. How far does the ball travel horizontally before hitting the ground? Round to the nearest tenth of a foot. c. Graph the function that models the ball’s parabolic path.

The quadratic function – 0.376(x − 45)² + 2.65(x − 45) — 3.84 gives the percentage (in decimal form) of puffin eggs that hatch during a breeding season in terms of x, the mean sea surface temperature of the surrounding area, in degrees Fahrenheit. a. What is percentage of puffin eggs that will hatch at 48°F? Round your answer to the nearest tenth of a percent. % b. For what mean temperature is the percentage of hatched puffin eggs a maximum? Round your answer to the nearest tenth of a degree. °F Find the percentage of hatched eggs at this temperature. Round your answer to the nearest tenth of a percent. %

Evaluating and Solving Quadratic Functions Duffer McGee stood on a hill and used a nine iron to hit a golf ball that reached a maximum height of 138 feet and stayed in the air for 5.5 seconds before it touched the ground. Pretty good for a Duffer. Mars has a gravity of approximately 12 feet per second squared compared to Earth's 32 feet per second quared. NASA did a simulation to try to determine how high the golf ball would fly and how long it would stay in the air on Mars if it was hit at the same height, angle and velocity as Duffer's. The data below represent the results of that simulation: t 1 2 3 4 5 H(t) 110 173 224 263 290 Use the Quadratic Regression feature of your calculator to generate a mathematical model for this situation. Write the function below. Round each coefficient to the nearest whole number. H(t) Based on your model how high is the hill from which the golf ball was hit?? The golf ball was hit from a hill feet high. Jse your model to estimate how long the golf…