2nd Summative Test - Mathematics 9 1ST Grading Name: ________________________ Grade & Section: ______________ Teacher: _____________ Date: ________ I. Directions: Read and analyze each question. Solve the problem and write the letter of the best answer. _____1. The sum and the product of the roots of a quadratic equation are 5 and 6, respectively. What is its equation? A. x2 + 5x - 6 =0 B. x2 - 5x + 6 = 0 C. x2 + 6x – 5 = 0 D. x2+ 6x + 5 =0 ____ 2. With the given equation 3๐ฅ 2 – 16๐ฅ − 12 = 0, which of the following is the product of the roots? A. −12 B. −4 C. 4 D. 12 ____ 3. If the product of roots of the quadratic equation given below is 2, then find the value of m in the equation 2๐ฅ 2 + 3๐ฅ − ๐ = 0. A. -4 B. -2 C. 2 D. 4 ____ 4. Which of the following are the roots of the quadratic equation ๐ฅ 2 – 5๐ฅ − 24 = 0? A. -8 and -3 B. 8 and 3 C. -8 and 3 D. 8 and -3 ____ 5. Find the roots of quadratic equation, x2 + 5x + 3 = 0. −5+√13 −5−√13 5+√13 5−√13 √13−5 √13−5 5−√13 5+√13 A. , B. , C. ,D. , 2 2 2 2 2 2 4 4 2 ____ 6. Ian turns a page of a certain book and found out that it has an area of 96 ๐๐ and a perimeter of 40๐๐. What are the dimensions of the book? A.8๐๐ ๐๐๐ 12๐๐ B. 6๐๐ ๐๐๐ 16๐๐ C. 4c๐ ๐๐๐ 24๐๐ D. 2๐๐ ๐๐๐ 48๐๐ ____ 7 The sum of the ages of Ethan and Joy is 30 and the product is 224. What equation can be used to find their ages? A. ๐ฅ 2 + 30๐ฅ + 224 = 0 C. ๐ฅ 2 − 30๐ฅ − 224 = 0 2 B. ๐ฅ − 30๐ฅ + 224 = 0 D. ๐ฅ 2 + 30๐ฅ − 224 = 0 2 ____ 8. In y = x – 4, what are the values of y? A. -4, -3, 0 B. 4, 3, 0 C. -3, 0, 5 D. -3, -4, 0 ____ 9. Which of these represents a quadratic function? A. y = x2 B. y = 2x C. y = 2x D. y = x3 ____ 10. The graph of a quadratic function y = ax2 + bx + c is called __________. A. bar graph B. line C. pie graph D. parabola ____ 11. Which of the following graphs represent y = x2 - 2x? ____ 12. Express the quadratic function y = x2 + 2x – 1 in the form y = a (x – h)2 + k. A. y = (x +1)2 + 1 C. y = (x + 1)2 - 2 2 B. y = (x + 1) + 2 D. y = (x + 1)2 – 1 2 ____ 13. Pepe and Pedro transform y = 3x – 12x + 16 to vertex form. Pepe’s answer is y = 3(x-2)2 +4 and Pedro’s answer is y = 3 (x +2)2 + 4. Who do you think got the correct answer? A. Pepe B. Pedro C. Both of them D. None of them ____ 14. What is f(x) = -3(x + 2)2 + 2 when written in the form of f(x) = ax2 + bx + c? A. f(x) = -3x2 + 12x – 10 C. f(x) = -3x2 + 12x + 10 2 B. f(x) = 3x – 12x + 10 D. f(x) = -3x2 –12x – 10 ____ 15. What is y = (x – 2)2 - 14 when written in the form y = ax2 + bx + c? A. y = x2 + 4x + 10 C. y = x2 + 4x - 10 2 B. y = x – 4x + 10 D. y = x2 - 4x – 10 ____ 16. Which statement is TRUE for the parabola whose equation is y = x2 – 6x + 15? A. The parabola opens upward C. The parabola contains the point (1,5) B. The line of symmetry is x=1 D. The vertex is (1,16) ____ 17. What is the vertex of the graph of y= x2 - 2x – 1? A. (-1,-2) B.(1,2) C.(1,-2) D. (-1,2) ____ 18. The vertex of the graph given on the right is on the ___________. A. base C. origin B. domain D. range ____ 19. Which of the following equations represents the graph? A. f(x) = -x2 C. f(x) = -(x+1)2 2 B. f(x) = x D. f(x) = (x + 1)2 ____20. In f(x) = x2 -4x -10, give the values of a, h and k. A. a = 1, h = 2 k =-14 B. a = 1, h = 2 k =14 C. a = -1, h = 2 k =-14 ____ 21. The graph of y = x2 – 7 is obtained by sliding the graph of y = x2 A. 7 units downward B. 7 units upward C. 7units to the right D. a = 1, h = -2 k =-14 D. 7 units to the left FOR NUMBER 22-23 From a 96-foot building, an object is thrown straight up into the air then follow a trajectory. The height S(t) of the ball above the building after t seconds is given by the function S(t) = 80t – 16t2. ____ 22. What maximum height the object reach? A. 196ft B. 169ft ____ 23. Find the time at which the object is on the ground? A. 5 seconds B. 6 seconds C. 100ft D. 96ft C. 7 seconds D. 8 seconds ____24. Find the zeros of the quadratic function y = x2 – 3x + 2. A. -1 and -2 B. 1 and 2 C. 1 and -2 D. -1 and 2 ____25. Find the zeros of y = 2x2 + 2x -24 A. 3 and -4 B. -3 and -4 C. 3 and 4 D. -3 and 4 ____26. In what direction does the graph of the quadratic function ๐ฆ = 3๐ฅ 2 − 7๐ฅ + 5 open? A. upward B. downward C. to the left D. to the right ____27. What is the vertex of the quadratic function ๐ฆ = ๐ฅ 2 − 2๐ฅ − 1? A. (1, −2) B. (−2, 3) C. (−2, −1) D. (2, −1) ____28. The graph of ๐ฆ = ๐ฅ 2 − 9 is obtained by sliding the graph of ๐ฆ = ๐ฅ 2 ________. A. B. 9 ๐ข๐๐๐ก๐ ๐๐๐ค๐๐ค๐๐๐ 9 ๐ข๐๐๐ก๐ ๐ข๐๐ค๐๐๐ C. 9 ๐ข๐๐๐ก๐ ๐ก๐ ๐กโ๐ ๐๐๐โ๐ก D. 9 ๐ข๐๐๐ก๐ ๐ก๐ ๐กโ๐ ๐๐๐๐ก For questions 29-30. Refer to the figure below. ____29. What is the vertex of the graph? A. (1, −3) B. (−3,1) C. (2, −3) D. (2,3) C. ๐ฅ = 2 D. ๐ฅ = 4 ____30. What is the axis of symmetry? A. ๐ฅ = −3 B. ๐ฅ = 1 II.Directions: Determine the nature, sum and product of the roots of the following quadratic.