Accel. Geometry FINAL EXAM REVIEW - UNITS 2 AND 3

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1 ccel. Geometry FINL EXM REVIEW - UNITS N 3 Name: ate: 1. Solve: x + 9 = 0 over the set of complex numbers.. ±9i. 3 + i. ±3i The altitude of a triangle is 4 cm more than the base. The area is 36 cm. Which equation best represents the situation where x represents the altitude of the triangle?. x(x 4) = 36. x(x + 4) = 36. Find the roots of x 4x + 6 = 0. x(x 4) = 36. x(x + 4) = 36. ± i. 4 ± i. ± i. ± i 3. Use the quadratic formula to find the roots of x x + 5 = The length of the side of a square is increased by 3 resulting in an area of 361. Which equation best represents the situation if X represents the original length of the side of a square?. 1 + i and 1 i. + i and i. x + 6x 361 = 0. x 6x 361 = i and 1 i. + i and i. x + 6x 370 = 0. x + 6x 35 = 0 4. Which of the following is an example of a mathematical expression? I. 3x 7x + 1 = 19 II. x 9 1 III. 8x 4y 1. onsider solving x + 1x + 5 = 0 by completing the square. x + 1x + = 5 + What is the number that goes in the blanks? I only. II only. III only. II and III 13. Solve: 4x 64 = 0 5. ( x 3 ) 5 is equivalent to which expression?. x 15. x. x 1. x 0.6. {8, 8}. {4, 4}. {0, 8, 8}. {4, 8, 8} 14. What are the solutions of the equation (x + 4)(x 15) = 0? 6. Simplify: ( 3y 5 ) 3. 9y 8. 9y 15. 7y 15. 7y 15. {4, 15}. {4, 15}. { 4, 15}. { 4, 15} 7. Simplify: (4n 3 )(n ) 15. Solve: c + 16c + 4 = 0. 6n 5. 8n 5. 6n 6. 4n 5. or 8. or 6. 6 or 8. 0,, or 1 8. Factor: x + 7x + 1. (x + 4)(x + 3). (x + 1)(x + 1). (x + 7)(x + 5). (x 4)(x 3) 9. Factor: 3q + q 16. Solve: (d + 3) = 7. {±}.. { } 7 ± 3. { ± 10 } { 3 ± 7 }. (3q 1)(q 1). (3q + )(q 1). (3q )(q + 1). (3q 1)(q 1) page 1

2 17. Which of the following functions has roots 5 ± ?. x + 3x + 5 = 0. x + 5x + 3 = 0 3. What are the roots of the function whose graph is shown?. {, }. {0, 4}. {0}. {4}. 3x + x + 5 = 0. 5x + 5x + 3 = Find the value of the discriminant of the quadratic equation 3x + x + 1 = State the vertex and x-intercept(s) of the given graph. 19. If the discriminant of the equation ax + bx + c = 0 is positive (a, b and c being integers), then the roots of the equation must be.. positive. rational. equal. real 0. What are the approximate roots of this equation? x 6x + 4 = 0. { 0.6, 6.6}. { 5.4, 0.76}. {0.8, 5.}. {3, 5} 1. Which is a solution for the following system of equations?. vertex: ( 1, 4) x-intercept(s): 3, 1. vertex: ( 4, 1) x-intercept(s): 1, 3. vertex: ( 3, 1) x-intercept(s): 1, 4. vertex: ( 3, 1) x-intercept(s): 4, 1 y = x y = 4x (6, 36). ( 6, 4). (, 4). (, 4). How many solutions are shown by the graph of the quadratic function? What is the domain of the function shown?. x 4. 4 < x < 6. { 4, 3,, 1, 0, 1,, 3, 4, 5, 6}. all real numbers. zero. one. two. three page ccel. Geometry FINL EXM REVIEW - UNITS N 3

3 6. What is the range of the relation? 30. Which of the following is the equation of the circle shown?. (x + 1) + (y ) = 16. (x 1) + (y + ) = 4. (x + 1) + (y ) = 4. (x 1) + (y + ) = y 1. y 3. { 3, 1}. all real numbers 31. Which one of the following relations defines a circle with radius 3?. x 3 + (y 3) = 1. x + y = 9 7. Which of these is a reasonable equation for the graph?. f (x) = 1 x. f (x) = 1 x. f (x) = x + 9. f (x) = x + 9. y = x + 3. x + y = 3 3. What is the equation of the circle with radius 4 and center (0, 3)?. x + (y + 3) = 16. x + (y + 3) = 4. x + (y 3) = 4. x + (y 3) = omplete the square to find the standard form for this circle: 8. The parabola shown in the graph can also be represented by. y = 1 (x 3) 4. y = 1 (x + 3) 4. y = (x 3) 4. y = (x + 3) 4 x + 4x + y + 16y 0 = 0. (x + 4) + (y + 8) = 0. (x + ) + (y + 8) = 0. (x + ) + (y + 8) = 3. (x + ) + (y + 8) = Find the center and radius of the circle x + y + 4x 6y + 1 = 0.. (, 3); 3. (, 3); 3. (, 3); 1. (, 3); 1 9. Given the graph below for f (x) and the equation g(x) = 3x 1x + 17, which has the greater minimum? 35. The graph of the equation 3x + 1x 0y + 4 = 0 is:. a parabola. an ellipse. a circle. a hyperbola 36. Given a parabola with directrix x=5 and vertex at (, -3), what is the coordinates of the focus and what direction does the parabola open?. g(x); minimum = 17. f (x); minimum = 0. f (x); minimum = 4. g(x); minimum = 5 page 3 ccel. Geometry FINL EXM REVIEW - UNITS N 3

4 37. Re-write in the parabola in standard form: 3x 30x y + 73 = 0. y = 3(x + 5). y + = 3(x 5). y + = 3(x + 5). y = 3(x 5) page 4 ccel. Geometry FINL EXM REVIEW - UNITS N 3

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