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Name: __________________________________________ Int Math 3 Review Handout (Sec.3-1 thru 3-7) 2 Graph each function. How is each graph a translation of f(x) = x ? 1 2 y = (x + 3) + 4 A C f(x) translated down 4 unit(s) and translated to the left 3 unit(s) f(x) translated up 4 unit(s) and translated to the right 3 unit(s) B D f(x) translated up 4 unit(s) and translated to the left 3 unit(s). 2 f(x) translated down 4 unit(s) and translated to the right 3 unit(s) 2 Which expression is equivalent to −x + 8x + 75 = 13? A B (x − 13)(x − 5) = 13 −(x − 13)(x + 5) = 3 −(x − 5)(x + 13) = 3 (x + 5)(x + 13) = 13 C D 1 Name: ______________________ 3 4 ID: A 2 Which is the graph of y = −2(x − 2) − 4? A C B D Identify the vertex and the axis of symmetry of the graph of the function 2 y = 2(x + 2) − 4. A B C D What is the maximum or minimum value of the function? What is the range? 5 vertex: (–2, –4); axis of symmetry: x = −2 vertex: (–2, 4); axis of symmetry: x = −2 vertex: (2, 4); axis of symmetry: x = 2 vertex: (2, –4); axis of symmetry: x = 2 2 y = 2x + 28x − 8 A B C D 2 minimum value: 7 range: y ≥ 7 minimum value: –106 range: y ≥ −106 minimum value: –7 range: y ≥ −7 minimum value: –106 range: y ≥ −7 Name: ______________________ 6 7 Suppose a parabola has an axis of symmetry at x = 8, a maximum height of 1 and also passes through the point (9, –1). Write the equation of the parabola in vertex form. 2 A y = −2(x + 8) + 1 B y = 2(x − 8) − 1 2 2 C y = (x − 8) + 1 D y = −2(x − 8) + 1 2 Identify the maximum or minimum value and the domain and range of the 2 graph of the function y = 2(x + 2) − 3. A B C D 9 ID: A 8 minimum value: –3 domain: all real numbers range: all real numbers ≥ −3 maximum value: –3 domain: all real numbers ≤ −3 range: all real numbers minimum value: 3 domain: all real numbers ≥ 3 range: all real numbers maximum value: 3 domain: all real numbers range: all real numbers ≤ 3 Use the vertex form to write the equation of the parabola. 2 A y = 3(x + 2) + 2 B y = 3(x − 2) + 2 C y = 3(x − 2) − 2 D y = (x + 2) + 2 2 2 2 You live near a bridge that goes over a river. The underneath side of the bridge is an arch 2 that can be modeled with the function y = −0.000495x + 0.619x where x and y are in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch? A The bridge is about 193.52 ft above the river and the length of the bridge above the arch is about 625.25 ft B The bridge is about 1250.51 ft above the river and the length of the bridge above the arch is about 193.52 ft C The bridge is about 1250.51 ft above the river and the length of the bridge above the arch is about 625.25 ft D The bridge is about 193.52 ft above the river and the length of the bridge above the arch is about 1250.51 ft 3 Name: ______________________ ID: A What is the graph of the equation? 2 10 y = −2x + 2x + 2 A C B D What is the number of real solutions? 2 11 8x − 11x = −3 A B no real solutions two real solutions one real solution cannot be determined C D 4 Name: ______________________ ID: A 2 12 Compare the equation, y = 9x − 4x , the graph below, and the table below. Which has the steepest rate of change from x = 1 to x = 2, and what is its value? x –1 1 2 3 A graph, –1 B equation, − y 0 2 0 –4 1 3 1 2 C table, − D equation, –3 What is the expression in factored form? 2 2 13 16x + 8x A B C D 14 −4x + 8x + 32 4x(4x + 2) −4x(4x + 2) 4x(4x − 2) 4(4x + 2) A B C D 5 −4(x + 4)(x + 2) −4(x − 4)(x + 2) −4(x + 4)(x − 2) −4(x − 4)(x − 2) Name: ______________________ ID: A Solve the equation. 2 15 x + 18x + 81 = 25 –14 –4, –14 A B 14, 4 –4, 4 C D What are the solutions of the quadratic equation? 2 2 16 3x + 25x + 42 = 0 A –6, 3 1 B 6, − 2 7 1 C − , − 3 2 7 D –6, − 3 17 4x − 18x + 20 = 0 A 2, 4 5 B ,2 2 C –2, 2 5 D 2, 2 Solve by using tables. Give each answer to at most two decimal places. 2 2 18 −7x − 2 = −10x A B C D 19 The function h = −10t + 95 models the path of a ball thrown by a boy where h represents height, in feet, and t represents the time, in seconds, that the ball is in the air. Assuming the boy lives at sea level where h = 0 ft, which is a likely place the boy could have been standing when he threw this ball? –0.47, 0.47 0.24, 1.19 –1.19, –0.24 0.48, 2.38 A B C D What value completes the square for the expression? 2 20 x − 18x A B 81 −9 9 −81 C D 6 a ladder a bridge an underground cave his backyard Name: ______________________ ID: A Solve the quadratic equation by completing the square. 2 2 21 x + 10x + 14 = 0 C −5 ± 11 5 ±6 −10 ± 6 D 100 ± A B 22 −3x + 7x = −5 11 67 A 7 ± 3 B − 7 ± 3 109 C − 7 ± 6 22 D 7 ± 6 3 3 6 109 6 Rewrite the equation in vertex form. Name the vertex and y-intercept. 23 2 y = x − 12x + 34 A B 2 y = (x − 12) − 2 vertex: (–12, –2) y-intercept: (0, –2) 2 y = (x − 6) − 2 vertex: (6, – 2) y-intercept: (0, 34) 2 y = (x − 12) + 40 vertex: (–12, –2) y-intercept: (0, –2) 2 y = (x − 6) + 70 vertex: (6, – 2) y-intercept: (0, 34) C D Use the Quadratic Formula to solve the equation. 2 2 24 −2x − 5x + 5 = 0 25 −4x + x = −4 32 A − 5 ± 4 B − 5 ± 4 C − 4 ± 5 130 D − 5 ± 2 65 2 65 4 4 2 7 A 1 ± 8 B 8± C 8± D 1 ± 4 65 8 130 8 65 8 65 4 Name: ______________________ ID: A Use graphing to find the solutions to the system of equations. 26 ÔÏÔ ÔÔ ÔÔ y = x 2 + 7x + 7 ÌÔÔ ÔÔ ÔÔÓ y= x + 2 A C (–5, 3) (–1, –1) B (–4, –3) (–2, –1) D (–4, 3) (–2, 1) (–5, –3) (–1, 1) 8 Name: ______________________ ID: A What is the solution of the quadratic system of equations? 27 ÔÏÔ ÔÔ ÔÔ y = x 2 + 18x + 35 ÔÌÔ ÔÔÔ y = −x 2 + 2x + 5 ÔÓ A B (–3, 98) (–5, 150) (–3, –10) (–5, –30) (–10, –3) (–30, –5) (3, –10) (5, –30) C D What is the solution of the system of inequalities? 28 ÔÏÔ ÔÔ ÔÔ y ≥ x 2 + 2x + 2 ÔÌÔ ÔÔ ÔÔ y < −x 2 − 4x − 2 Ó A C B D 9