The document consists of a series of mathematical problems and questions focusing on quadratic equations, their solutions, properties, and graphs. It includes multiple-choice questions about roots, equations, areas, mathematical relationships, and inequalities. Various scenarios require the application of foundational algebra concepts to derive answers.

1. Direction: Choose the letter that corresponds to
the correct answer. Write your answer in the
space provided before each number.

2. 1. In the quadratic equation ( + 5)
𝑦
( – 5) = 4, what are the values of
𝑦
, , ?
𝑎 𝑏 𝑎𝑛𝑑 𝑐
A. a = 1, b = 5, c = -5 C. a = 1, b = 0, c = -29
B. a = 1, b = - 5, c = 5 D. a = 1, b = 0, c = 25

3. 2. Find the solutions of the
following equation − 3 − 40 = 0.
𝑥
A. -5 and -8 C. -5 and 8
B. 5 and -8 D. 5 and 8

4. 3. Solve for x by extracting square
roots, = 256
A. 14 and -14 C. 16 and -16
B. 23 and -23 D. 18 and -18

5. 4. In the equation − 12 = 0, the
roots are?
A. 2 and -2 C. 4 and - 4
B. 3 and -3 D. none of these

6. 5. In the equation + 7 − 120 = 0,
𝑥
the solutions are?
A.12 and -10 C. 15 and -8
B. - 20 and 6 D. 8 and -15

7. 6.What is the nature of the roots of a
quadratic equation where − 4 = 0?
𝑎𝑐
A. Real, rational and equal
B. Real, irrational and not equal
C. Real, rational and not equal
D. No real roots

8. 7. What are the values of the
discriminants for the quadratic equations
with real, irrational and not equal roots?
A. – 4ac = 0
B. – 4ac < 0
C. – 4ac > 0 but not perfect square
D. – 4ac > 0 and perfect square

9. 8. What is the value of in − 3 −
𝑘 𝑘 𝑥
10 = 0 if its discriminant is 89?
A. -2 B. 0 C. 1 D. 2

10. For # 9 – 11. Problem: Anna wants to make a wooden
rectangular frame with an area of 450 and a
perimeter of 90 in. What should be the dimension of
the frame?
9. What equation represents the area of the frame
in terms of its width?
A. + 45 − 450 = 0 C. − 45 + 450 = 0
𝑤 𝑤
B. + 90 − 450 = 0 D. − 90 + 450 = 0
𝑤 𝑤

11. For # 9 – 11. Problem: Anna wants to make a wooden
rectangular frame with an area of 450 and a
perimeter of 90 in. What should be the dimension of
the frame?
10. What is the relationship of the sum of roots of the
equation in #9 to the given perimeter?
A. The sum of roots is half the perimeter.
B. The sum of roots is twice the perimeter.
C. The sum of roots and the perimeter are equal.
D. The sum of roots is the negative of one half the perimeter

12. For # 9 – 11. Problem: Anna wants to make a wooden
rectangular frame with an area of 450 and a
perimeter of 90 in. What should be the dimension of
the frame?
11. What should be the dimension of the
frame?
A. 18 in by 25 in C. 5 in by 90 in
B. 15 in by 30 in D. 6 in by 75 in

13. 12. Which of the following rational
algebraic equations is transformable
to a quadratic equation?

14. 13. Given , , are real numbers
𝑎 𝑏 𝑎𝑛𝑑 𝑐
and ≠ 0, which of the following is the
𝑎
standard form of quadratic equation?
A.+ + = 0 C. = +
𝑏𝑥 𝑐 𝑎 𝑏𝑥 𝑐
B. + + = 0 D. +
𝑎𝑥 𝑏𝑥 𝑐 + = 0
𝑐

15. 14. Express ( + 7)( − 2) = 0 in
𝑤 𝑤
standard form
A. + 5 + 14 = 0 C. + 5 − 14 = 0
𝑤 𝑤
B. − 5 − 14 = 0 D. − 5 + 14 = 0
𝑤 𝑤

16. 15. Express in simplest form.

17. 16. If a number is added to its
square, the sum is 20. Find the
number.
A.3 B. 4 C. 5 D. 6

18. For question nos. 17– 19, refer to the problem below.
Pedro is a well-known carpenter in Maragusan, Davao de Oro. He
works in one of the hotels in the same place. One morning, he cut the
25 electric wire into two parts in such a way that the sum of their
𝑚
reciprocals is
17.Which of the following is the longest
part of the electric wire?
A. 5 B. 10 C. 15 D. 20

19. For question nos. 17– 19, refer to the problem below.
Pedro is a well-known carpenter in Maragusan, Davao de Oro. He
works in one of the hotels in the same place. One morning, he cut the
25 electric wire into two parts in such a way that the sum of their
𝑚
reciprocals is
18. What are the measures of the two parts of the
electric wire?
A. 5 & 10 B.10 & 15 C. 15 & 20 D. 20 & 25

20. For question nos. 17– 19, refer to the problem below.
Pedro is a well-known carpenter in Maragusan, Davao de Oro. He
works in one of the hotels in the same place. One morning, he cut the
25 electric wire into two parts in such a way that the sum of their
𝑚
reciprocals is
19. What quadratic equation can be derived from
the given problem?

21. 20. Which of the following coordinates of
points belong to the solution set of the
inequality y < + 3x − 5?
A. (-2, 9) C. (-1, 5)
B. (-3, 2) D. (1, 6)

22. 21. The figure below shows the graph of y < − 4x − 1. Which of the following is true
about the solution set of the inequality?
I. The coordinates of all points along the parabola as shown by the broken line
belong to the solution set of the inequality.
II. The coordinates of all points on the shaded region belong to the solution set of
the inequality.
III. The coordinates of all points along the parabola as shown by the broken line do
not belong to the solution set of the
inequality.
A. I and II
B. I and III
C. II and III
D. I, II and III

23. For items 22–23, read the problem carefully and
choose the letter of the best answer. The longer leg of a
right triangle is 1 inch more than the other leg. What
are the possible lengths of the legs so that the
hypotenuse is at most 5 inches?
___22. Which of the following mathematical
sentences represents the hypotenuse?
A. c ≥ 5 B. c ≤ 5 C. c > 5 D. c < 5

24. For items 22–23, read the problem carefully and
choose the letter of the best answer. The longer leg of a
right triangle is 1 inch more than the other leg. What
are the possible lengths of the legs so that the
hypotenuse is at most 5 inches?
23. Which of the following is the mathematical
sentence of the given problem?

25. 24. Which graph represents a
quadratic function?

26. 25. What direction does the parabola
open if the quadratic term of the
equation is positive?
A. downward C. right side
B. left side D. upward

27. 26. Which ordered pair represents
the function ( ) = – 3 + 2?
𝑓 𝑥 𝑥
A.(-5, 0) C.(-4, 0)
B.(0, 3) D.( 0 ,2)

28. 27. What is the vertex of the graph
on the right?
A. (2, 1)
B. (3, - 2)
C. (4, – 3)
D. (5, – 2)

29. 28. In the equation − 6 − 7 = 0,
𝑥
what constant do you add to the
trinomial in order to become a
perfect square?
A. −81 B. −9 C. 9 D. 81

30. 29. What is of the quadratic
𝑘
function y = + 4x + 2 if h = − ?
A. B. C. D.

31. 30. What is the domain of the given
quadratic function =
𝑦 ?
A. all positive real numbers
B. all real numbers
C. all negative real numbers
D. all non-real numbers

32. 31. If the minimum point of the
function = + 10 + 9 is (−5, −16),
𝑦 𝑥
what is the equation of its axis of
symmetry?
A. 𝑦 = −5 C. = −5
𝑥
B. = −16
𝑦 D. = −16
𝑥

33. 32. Which of the following shows the
graph of ( ) = 2 – 3?
𝑓 𝑥

34. 33. What is the domain of this quadratic
function: f(x) =−2 − 5?
A. The set of all Natural Numbers
B. The set of all integers
C. The set of all Whole Numbers
D. The set of all Real Numbers

35. For numbers 34 – 36, refer to the graph
given below
34. What is the vertex of the parabola?
A. (-1, 2) C. (2, -1)
B. (1, -2) D. (-2, 1)

36. For numbers 34 – 36, refer to the graph
given below
35. What are the x-intercepts of the
graph?
A. 0 and 1 C. 3 and 2
B. 3 and 0 D. 1 and 3

37. For numbers 34 – 36, refer to the graph
given below
36. What is the range of the given graph?
A. {y: y ≤ −1} C. {y: y ≤ 2}
B. {y: y ≥ −1} D. {y: y ≥ 2}

38. 37. What is the quadratic function f(x)
whose zeros are 2 and -7?
A. 𝑓( ) = + 5 − 14
𝑥 𝑥
B. ( ) = − 5 + 14
𝑓 𝑥 𝑥
C. ( ) = − 5 − 14
𝑓 𝑥 𝑥
D. ( ) = + 5 + 14
𝑓 𝑥 𝑥

39. 38. An object is thrown vertically upward
with a velocity of 80 / . The distance
𝑚 𝑠𝑒𝑐
( ) above the ground after seconds is
𝑆 𝑡 𝑡
given by the formula ( ) = 80 − 5 .
𝑆 𝑡 𝑡
How long will it take the object to reach
the ground?
A. 4 seconds C. 7 seconds
B. 5 seconds D. 8 seconds

40. 39. What is the graph of a quadratic
function?
A. Circle
B. Line
C. Parabola
D. V-Shape

41. 40. Which quadratic function opens
upwards and has a vertex of (0,3)?
A. 𝑦 = −
B. =
𝑦
C. = + 3
𝑦
D. = (+ 1) + 3
𝑦