Calculator Handbook I. How to Find Zeros on the Calculator

Practice Use your calculator to find the zeros of the following functions a. 𝑦 = 𝑥! − 10𝑥 + 16

b. 𝑦 = 𝑥! − 4𝑥 − 32

c. 𝑦 = 2𝑥! + 𝑥 − 15

d. 𝑦 = 21𝑥! − 62𝑥 + 16 *To change your roots to a fraction

Press 2ndà QUIT to clear the screen

Press Enter The first root will be stored as x

Then Press XàMATHàFrac To convert to a fraction

Calculator Handbook II. Using Zoom Fit, Value, and Maximum functions Example. Martin wants to launch a water balloon off of a rooftop. The height, in feet, the balloon is above the ground is modeled by the equation ℎ 𝑡 = −16𝑡! + 96𝑡 + 112. a. Let 𝑥 = 𝑡 and 𝑦 = ℎ(𝑡), then enter the equation into “Y =” b. Set an appropriate domain by pressing WINDOW (remember that x represents time) X Min = X Max = ZOOM à 0:ZoomFit c. Micro-adjust the y values to create a better window and press GRAPH d. How high is the balloon from the ground when it is released from his hand? (𝑡 = 0) 2NDàCALCàVALUEà0 e. At what time and height does the balloon reach a maximum? 2NDàCALCà4: maximum Left Bound? Move the curser to the left of the maximum and press ENTER Right Bound? Move the curser to the right of the maximum and press ENTER Guess? ENTER f. At what time does the ball hit the ground? 2ndàCALCà 2:zero Left Bound? Move the curser to the left of the zero and press ENTER Right Bound? Move the curser to the right of the zero and press ENTER Guess? ENTER

a.

b.

c.

d.

e.

f.

Algebraically Solve the same problem To find the initial height, set 𝑡 = 0

To find the maximum, find (− !!!, ℎ(− !

!!))

To find the zeroes, set ℎ 𝑡 = 0 and solve by factoring. Remember to reject the extraneous solution outside of a real world domain

Calculator Handbook Practice. Find the initial height, maximum, and zeros of the following functions in a real world domain. a. The empire state building is 1250 feet tall. If an object is thrown upward from the top of the building at an initial velocity of 38 feet per second, its height s seconds after the ball is thrown, is given by the function ℎ 𝑡 = −16𝑡! + 38𝑡 + 1250, determine the initial height, the maximum height, and when the ball hits the ground. b. A juggler is tossing a ball on a path given by the function ℎ 𝑡 = −16𝑡! + 15𝑡 as the ball moves from the left hand to the right hand, 5 feet above the ground. Determine the maximum height and how long the ball is in the air. Deltamath Practice Refer to assignment 2.8 - Finding Roots Graphically c. Maximum Profit: A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using the equation 𝑦 = −𝑥! + 64𝑥 − 340, find out the maximum amount of profit the company can make, to the nearest dollar. d. Breaking Even: A company sells widgets. The amount of profit, y, made by the company is related to the selling price of each widget, x, by the given equation. Using the equation 𝑦 = −𝑥! + 82𝑥 − 665, find out how much the widgets would have to be sold for, to the nearest cent, in order for the company to break even. Only enter one possible price.