Algebra: 10.3.1: Intersect or Intercept? Name Solutions Block Date Bell Work: a. = 4 2 3 = 3 2 3(4 ) = 3 2 12 + 3 = 3 5 12 = 3 5 = 15 Solve each sstem b substitution or elimination. Check our solutions. (3, 1) = 3 = 4 3 = 1 b. + 2 + 3 = 6 3 = 12 3 = 18 = 6 2(6) + 3 = 6 12 + 3 = 6 3 = 6 = 2 (6, 2) c. + 5 = 8 4 + 3 = 2 = 8 5 4(8 5) + 3 = 2 32 20 + 3 = 2 32 17 = 2 17 = 34 = 2 ( 2, 2) = 8 5(2) = 8 10 = 2 10-97. Graph the parabola with equation = 2 3 4 and the line with equation = 2 + 2 on the grid. a. Name all - and -intercepts for the parabola. b. Name all - and -intercepts for the line. c. Where do the graphs intersect each other? d. The words intersect and intercept look and sound a lot alike, but what do the mean? How are the alike? How are the different?
10-98. Intercepts and intersections are similar, but the are not eactl the same. How can ou tell which one ou are looking for? Read the situations below and decide if the graphical solution would best be represented as an intercept or an intersection. Be prepared to defend our decision. Note: You do not need to solve the problem! a. A 5-gram candle on a birthda cake is lit. Two minutes after it is lit, the candle weighs 4.2 grams. How long will the candle burn? b. A local bowling alle charges ou $4 to rent shoes and $3.50 for each game ou pla. Another alle charges ou $7 to rent shoes and $2 for each game ou pla. How man games would ou need to pla in order for both alles to charge ou the same amount? c. Two months after Alia's birthda, she had $450, while her sister Claudia had $630. Five months after her birthda, Alia had $800, while Claudia had $920. How much did each person have on Alia's birthda? 10-99. Using a graph to find the intersection of two curves can be challenging when the point of intersection is not on gridlines or ends up off the graph. Therefore, it helps to know another wa to find the intersection without using a graph. a. Name the algebraic methods ou alread know to solve linear sstems. b. Use one of the methods ou listed in part (a) to solve for the intersection of = 2 3 10 and = 2+ 2. Carefull record our steps. Be sure to check our results along the wa. Does the graph in problem 10-97 confirm our results?
10-100. Solve the sstem of equations below for and. Write our solution(s) in the form (, ). Then graph the sstem with our graphing calculator and confirm our solution. = 1 = 2 + 1 [ 1 = 2 + 1] 1 = 2 2 + 0 = 2 2 + 1 1 1 1 2 2 2 2 +1 + 1 = 0 = 1 2 1 = 0 2 = 1 = 1 2 = 1 1 = 1 = 1 1 2 = 2 ( 1, 1) ( 1 2, 2) 10-101. Algebraicall find the intersection of the two functions below. Then graph the sstem on the grid and confirm our solution. 2 + 4 + 5 = + 1 = + 1 2 = 2 + 3 + 4 = 0 + 4 + 5 = b ± b2 4ac 2a = 3 ± 32 4(1)(4) 2(1) = 3 ± 7 2 No Real Solutions 10-102. Use the graph to identif intercepts and points of intersection for the two functions. a. Intercepts ( 2, 0) (5, 0) (8, 0)(0, 5) (0, 9) b. Points of Intersection (1, 8) (4, 5) c. What is the difference between intercepts and points of intersection? Intercepts are where a function crosses the ais or the ais. Points of intersection are points where the two graphs cross. 10-103. You alread found the solution to the equation 2 3 10 = 2 + 2 using algebra in problem 10-99. Show and Eplain where these solutions are found in the graph to the right. The points where the two graphs intersect
10-104. Algebraicall solve the sstem of equations below for and (Use Substitution) Write our solution(s) in the form (, ). Graph to confirm our solution(s). = 2 + 2.6 + 0.45 = 2 + 1 2 + 2.6 + 0.45 = 2 + 1 2 + 0.6 0.55 = 0 = b ± b2 4ac 2a = 0.6 ± (0.6)2 4(1)( 0.55) 2(1) = 0. 5, = 1. 1 (0.5,2) ( 1.1, 1.2) 10-105. Without doing an more solving, what is the solution to 2 + 2.6 + 0.45 = 2 + 1? Verif our solution b checking in the equation. = 0. 5, and = 1. 1 (0.5) 2 + 2.6(0.5) + 0.45 = 2(0.5) + 1 2 = 2 ( 1.1) 2 + 2.6( 1.1) + 0.45 = 2( 1.1) + 1 1.2 = 1.2 10-106. The solution to ver comple equations can be estimated with graphs. Estimate the solution(s) b graphing in the calculator. How man solutions are there? 2 ( 3 4 ) + 7 = 0.7 4 + 38 6 3.1 There is one solution 10-107. Is = 7 a solution to 3( 2) 4? Show wh or wh not. No 3(7 2) 4 3(5) 4 15 4 False
10-108. Eamine the two lines graphed at right. Will these two lines intersect? Yes Find the equation of each line and graph in the calculator. Y 1 = 1 + 10 4 Y 2 = 1 3 + 3 Is there an intersection point? Yes If so, what is it? (12, 7) 10-109. For each line in problem 10-108, find the - and -intercepts. Y 1 Y 1 Y 2 Y 2 10-110. Which of the equations below is equivalent to 4(3 1) + 3 = 9 + 5? More than one ma be equivalent. Justif our answer(s) b solving each equation. 12 4 + 3 = 9 + 5 a. 12 4 + 3 = 9 + 5 15 4 = 9 + 5 b. 12 1 + 3 = 9 + 5 c. 11 = 14 0 = 3 0 = d. 15 4 = 9 + 5 15 1 = 9 + 5 6 1 = 5 6 = 6 = 1 6 4 = 5 6 = 9 = 3 2 10-111. Write an equation for the line passing through the points (4, 8) and ( 3, 12). Δ = 20 Δ 7 8 = 20 (4) + b 7 8 + 20 (4) = b 7 24 7 = b = 20 7 + 24 7
10-112. Graph f() = ( + 2) 2 + 3: a. How does it compare to the graph of = 2 The graph is inverted, moved left 2 and up 3 b. Where is the maimum value found on the graph? The -coordinate of the verte c. What is this maimum value? 3 10-113. The owner of Taco Shack saw reviews online complaining that there was not enough cheese on his tacos. Without identifing himself, he randoml purchased 250 tacos from his own stores and from his competitor. He weighed the amount of cheese on each taco. His results are below: a. Is there an association between the amount of cheese and where a taco was purchased? b. Should the owner of Taco Shack adjust the amount of cheese based on what his competitor is doing? 10-114. Use a graph in the calculator to find the solution(s) to + 3 = 2 4 Plug solutions into the equation to confirm our answer(s). 2.39 2.39 + 3 2( 2.39) 4. 781.78