DO NOW A video game company’s revenue is represented by the equation R = –12p2 + 400p + 15000 where p is the price in dollars of the video game. What price will maximize the revenue? Find the maximum revenue. A ball is thrown upward from a height of 13 ft. with an initial upward velocity of 9 ft/s. Use the formula h(t) = -15t2 + 9t + 13. how long will it take the ball to hit the ground

Evaluating polynomials and finding a functions rate of change 03/09/2015 SWBAT: Calculate the rate of change from an equation, a table, and in the context of a situation

Evaluating polynomials Evaluating polynomials is how we solve for the points that make up a graph Remember: x values are the inputs, y values are the output In order to evaluate a polynomial, we plug in a value for x and solve for the output y Remember order of operations and be careful with exponents and sign changes

"Evaluation" mostly means "simplifying an expression down to a single numerical value". Sometimes you will be given a numerical expression, where all you have to do is simplify.

Example Remember quadratics? x2 x y -3 -2 -1 1 2 3

Example We do the same thing with longer polynomials

Example

Example

Example f(x) = -3x3 - x2 + 9x – 6. Find f(4)

Practice

Rate of change from a function To find the rate of change between 2 values in a function Evaluate the function at each value Find the difference between the 2 evaluated values (outputs) Divide by the difference of the 2 original values (inputs) Remember to use the correct units in your answer

Example Let f(x) = 3x-5. Find the average rate of change of f between x = 0 and x = 1

Example Let f(x) = -3x3 - x2 + 9x – 6. Find the average rate of change of f between x = 2 and x = -4

Example The position p(t) of an object at time t in seconds along a line marked in meters is given by p(t) = 3t2 -5 Find the average velocity between 2 seconds and 4 seconds

Example The position of a bug at t (in minutes) along a line marked in centimeters is given by b(t) = t3 + 1 Find the average velocity of the bug between the times t = 2 and t = 4

Example A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba divers rate of change?

Practice Let f(x) = 9x-7. Find the average rate of change of f(x) between x = 2 and x = 5 Let f(x) = 12x +8. Find the average rate of change of f(x) between x = 3 and x = 7 Let f(x) = 5x3 - 2x2 + 4x – 1. Find the average rate of change of f(x) between x = 3 and x = -2 Let f(x) = -5x4 + 3x2 – 6. Find the average rate of change of f(x) between x = 7 and x= 3 If an object is dropped from a tall building, then the distance (ft) it has fallen after t seconds is given by the function d(t) = 16t2 – 3t + 2 . Find its average speed (average rate of change) between 3 seconds and 5 seconds.