Algebra I Quadratics Practice Questions
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1 1. Which is equivalent to ? Which is equivalent to 6 8? Which is equivalent to 7 6? Which is equivalent to 4? 8 6 From CCSD CSE S Page 1 of
2 Which is equivalent to 10? A class of students was told to compute the area of the rectangle below The class came up with three different values for the area: How many of those values correctly represent the area of the rectangle? The irrational numbers are closed under multiplication. For questions 8-9, classify each number as rational or irrational Rational From CCSD CSE S Page of
3 irrational rational irrational 10. Answer each part. (a) What is an irrational number? (b) Eplain why is an irrational number. 11. In each part, provide an eample of the statement. (a) The sum of two rational numbers is rational. (b) The product of a rational number and an irrational number is irrational. (c) The product of two irrational numbers can be rational. 1. Answer each part. (a) Write 4 as the product of a rational and an irrational number. (b) Give an eample where the product of two irrational numbers is a rational number. (c) Eplain why the sum of a rational number and an irrational number must be irrational. 1. Which epression is equivalent to c b yc yb? b y c c y b yb c Which is equivalent to 4 9y y y y y y y From CCSD CSE S Page of
4 For questions 15-17, use the epression 4 4 y. 15. y y is equivalent to the given epression. 16. y y y is equivalent to the given epression. 17. y y is equivalent to the given epression. For questions 18-19, use the equation p. 18. p 19. p 0. Let y and 6 y. What is the value of y? From CCSD CSE S Page 4 of
5 1. Which of these is NOT a factor of ? For question, consider the solutions to the equation has the same solutions as the given equation.. Given 4 8 c q, where c and q are integers, what is the value of c? Which quadratic equation has solutions of = a and = b? ab 0 b a ab 0 b a ab 0 b a ab 0 5. If 7 is a factor of k, what is the value of k? From CCSD CSE S Page 5 of
6 6. Factor The epression is not factorable with real coefficients. 7. Factor The epression is not factorable with real coefficients. 8. Which is a factor of ? Which equation has roots of 4 and 6? Which epression is equivalent to 40? From CCSD CSE S Page 6 of
7 1. Which epression is equivalent to ? What value of c makes the epression y 9y c a perfect trinomial square? Epand the epression Solve the equation u h P u P h for u, where all variables are positive real numbers. h P u u h P h u P From CCSD CSE S Page 7 of
8 For questions 5-6, use the scenario below. A rectangular playground is built such that its length is twice its width. w = w 5. The area of the playground can be epressed as w. 6. The perimeter of the playground can be epressed as 4w The quadratic equation is rewritten as p q. What is the value of q? What number should be added to both sides of the equation to complete the square in 8 17? If p 5 and q 16, which of these CANNOT equal p + q? 1 9 From CCSD CSE S Page 8 of
9 What value(s) of make the equation m n 0 true? (m and n do not equal zero.) m and n m and n mn 0 For questions 41-4, the quadratic equation 41. f can be written as a difference of squares. f c 0 has eactly one real solution c 8 4. Solve the equation for : a h k p p h k a p h k a h h p k a p k a From CCSD CSE S Page 9 of
10 44. Solve the quadratic = or = 1 = = 1 or = 4 1 or = 8 7 = 0 or = 45. The equation a < 0 a = 0 a > a has no real solutions. What must be true? 46. What is the solution set of the equation 4t 1 8? 1 1 1, 4 1,5 4 4, 5, How many real solutions does the equation 4 0 have? How many real solutions does the equation 0 1 y 0 have? From CCSD CSE S Page 10 of
11 49. What is the solution set of 4 5 9? 1 1, 4 9 1, , 4 4 There are no real solutions. 50. The graph of y 6 has how many -intercepts? Which shows the correct use of the quadratic formula to find the solutions of 8 1? What is the solution set for the equation ? 4, 7 7, 4 From CCSD CSE S Page 11 of
12 11,, What are the solutions of 6? What is the solution set of the equation 6 5 0? , , A quadratic epression has two factors. One factor is. In each part below, find another factor of the quadratic, if possible. If the situation described is not possible, eplain why. (a) The quadratic has no real zeros. (b) The quadratic has only one real zero. (c) The quadratic has two distinct real zeros. 56. Given a b c What are the values of a, b, and c? From CCSD CSE S Page 1 of
13 57. One way of epressing a quadratic function is f a b c. A second way is f a h k. (a) Find b in terms of a, h, and k. (b) Find c in terms of a, h, and k. 58. Find all solutions to the equation Show your work. 59. Solve each quadratic equation for. (a) 8 0 (b) 4 0 (c) The figure below shows a proposed sand pit, an area in a park that will be filled with sand. feet feet feet The sand pit is to be a large rectangular area twice as long as it is wide, plus a smaller rectangular area feet long and as wide as the large area. The two areas share a common side. (a) Write an epression for the total perimeter of the sand pit as a function of. (b) Write an epression for the total area of the sand pit as a function of. 61. Define and sketch the three quadratic functions that have the following characteristics. (a) f has an ais of symmetry at = and no -intercepts. (b) g has a y-intercept at and opens downward. (c) h has a zero at = and a minimum value of 6. From CCSD CSE S Page 1 of
14 6. A parabola is defined as f a what happens to the y-coordinate of the parabola s verte? it decreases it increases it does not change 10, where a is a positive real number. As a increases, 6. A parabola is defined as f a 10, where a is a positive real number. As a increases, what happens to the y-coordinate of the parabola s y-intercept? it decreases it increases it does not change 64. A quadratic function is defined as y The parabola has a maimum value of 7. The parabola has a minimum value of 7. The parabola has a maimum value of 4. The parabola has a minimum value of Which statement is true? 65. Solve the system of equations. y 4 6 y 5 ( 4, 6) (0, 5) ( 5, 5) and ( 1, ) ( 5, 5) (E) True (F) False From CCSD CSE S Page 14 of
15 66. The parabola y 9 and the line y = 8 intersect at two points. Which equation would be useful to find these points? (E) y 1 1 In questions 67-69, use the graph below. The graph shows the height h above the ground (in meters) of a thrown ball as a function of time (in seconds). h t 67. The ball hits the ground seconds after it is thrown. 68. Height begins decreasing as soon as the ball is thrown (t = 0). 69. The domain of the function that describes the height of the ball is all real numbers. From CCSD CSE S Page 15 of
16 70. A scientist drops an object from the top of and 80-foot building. The scientist uses a stopwatch to measure the time between when it was dropped and when it hits the ground. The height of the object above ground as a function of time is given by ht 80 16t. Which is the domain of this function? t can be any real number. t can be any positive real number. t can be any real number between 0 and 80, inclusive. t can be any real number between 0 and 5, inclusive. 71. What are the domain and range of the function y 6 8 shown in the graph below? Domain: all real numbers Range: y 1 Domain: all real numbers Range: all real numbers Domain: 4 Range: y 1 Domain: 4 Range: all real numbers From CCSD CSE S Page 16 of
17 7. Which of the following is the graph of y 4 5? 7. A quadratic function is given by h a b c, where a and c are negative real numbers. Which of these could be the graph of y h? y y y y From CCSD CSE S Page 17 of
18 74. Which is the graph of f? f() f() f() f() 75. Use the graph. y k = k = k = 1 Which equation defines this set of parabolas? From CCSD CSE S Page 18 of
19 y k 1 y k 1 y k Use the graph. Which equation is represented the following graph? y 6 y 6 y 6 y 6 For questions 77-79, consider the graph of y The graph opens up. 78. The ais of symmetry is at 5. 8 From CCSD CSE S Page 19 of
20 79. What is the verte of the parabola in the given equation? y 1 5, 41, 7, 55 6, Where is the ais of symmetry in the quadratic f 9 5 = 4 = = 6 = 81. Use the graph below. y? (, ) Which equation could define the given parabola, where a is a positive real number? f a f a From CCSD CSE S Page 0 of
21 f a f a In question 8, use the diagram and scenario below. 8. The table below is of the quadratic f f g 6 5. A second quadratic is defined as Which is true about the two functions minimum values? f has a smaller minimum value. g has a smaller minimum value. The minimum values of f and g are equal. Which function has the smaller minimum cannot be determined from the information given. 8. The graph of y 4 intersects a line at (p, 0) and (t, 5). What is the greatest possible value of the slope? Eplain your reasoning. f Use the function Show all work. (a) Identify the intercepts. (b) Identify the ais of symmetry. (c) Determine the coordinates of the verte. (d) Sketch the graph. (e) State the domain and range. 85. Answer each part. (a) Factor completely: 4 16 From CCSD CSE S Page 1 of
22 (b) Solve: (c) Graph (d) Solve the system f 4 16, and label key points and the ais of symmetry. y f and y 8. f Given (a) Complete the square for f. (b) Using the quadratic formula, eplain why the graph of y f has no -intercepts. From CCSD CSE S Page of
Algebra I Practice Questions ? 1. Which is equivalent to (A) (B) (C) (D) 2. Which is equivalent to 6 8? (A) 4 3
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