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Y-intercept: Beginning value Where graph crosses y-axis 3; The height of the ball at 0 seconds X-intercept, Zeros, Break-even point: Where graph crosses x-axis -1 second and 3 seconds f(2) : X-value is 2, find the y value 3 feet f(x) = 4: y value is 4 find the x value 1 second Increasing: The x-values where the graph is going up x < 1 second Decreasing: The y-value where the graph is going down x >1 second Maximum: ( , ) (1,4) Minimum: ( , ) None Height of a Ball Y-intercept Profit from Sally’s Lemonade Stand -4; She starts owing $4 Find Break-even point: 2 glasses of lemonade 2 glasses of lemonade Find and interpret f(5) : $6; She makes 6$ with 5 glasses sold Profit ($) X-intercept Find and interpret f(x) = 8: 6; She makes $8 selling 6 Glasses. Increasing: Always Solve by the graph: 2x – 4 = 10 7 Number of Glasses Sold Initial Value: They lose $5000 if ticket price is $0 Break-even point: Find and interpret f(2) : They make ~$1800 with a Ticket price of $2 Find and interpret f(x) = 40: They make $4000 with a ticket price of $3.50 or $6.50 Increasing: Profit (Hundred’s of Dollars) They start making money with Ticket price of $1.50 x < $5. Find and interpret the maximum: Projected Profit of Concert Based on Ticket Price Cost of Ticket ($) (5,50); Maximum profit is $5000 when ticket price is $5 When is -4x2 – 40x – 50 = 20? At x = $2.10 and $7.8 After how many miles will the companies be the same? Cost of Cab Rides 2 miles B is a better value until 2 miles. After two miles, A is a better value Find and interpret the y-intercept of A(x) and what does it mean? $5. Company A charges $5 for 0 miles Fare ($) Explain when each company is a better value. Find and Interpret B(2) $7 Company B charges $7 for 2 miles When is 3x + 1 = 4? 1 mile When is 3x + 1 = x + 5 2 miles Miles Stories Stair Stories Climbed by Two Climbers Time (minutes) Find and Intrepret Y-intercept Find Break-even point: X-intercept Find and interpret f(5) : Find and interpret f(x) = 6: Solve by the table: 2x – 2 = 4 Write the NEXT-NOW equation Profit of Selling Popcorn Bags x 0 1 2 3 4 5 Profit L1 -2 0 2 4 6 8 Y1=2x - 2 Y-intercept Profit of Selling Pompoms Find and interpret Break-even point: # of Pompoms Profit Find and interpret zeros Find and interpret f(4) : Find and interpret f(x) = -4: Solve by the graph: 3x – 7 = 2 x -1 0 1 2 3 4 'L1 -10 -7 -4 -1 2 5 Y = 3x - 7 After how many miles will the companies be Delivery Charges of 2 Companies the same? Explain when each company is a better value. A(x) Find and interpret the y-intercept of A(x) and what does it mean? Find and Interpret B(2) When is 2x + 3 = 2.5x + 1 When is 2x + 3 = 13? Write the NEXT-NOW equation for B(x) x 0 1 2 3 4 5 6 'L1 3 5 7 9 11 13 15 B(x) "L2 1 3.5 6 8.5 11 13.5 16 A(x) = 2x + 3 B(x) = 2.5x + 1 Starting Value Rate Increase or Decrease Decimal multiply by NEXT=NOW Statement $20,000 5% increase 100+5 = 105% =1.05 Or 1(20,000) + .05(20,000) Next=Now*1.05 starting at 20,00 $20,000 5 % decrease $100 4% interest 95,000 3.5% increase 1st 4 Numbers 8,6,4.5, Next = Now *1.095 starting at $1000 12,20,100/3 x 15% commission