1-quadratic equation 2-quadratic function
TRANSCRIPT
1-Quadratic Equation
2-Quadratic Function
Quiz No. 1
I. Identify which of the following equations are quadratic and not quadratic. Write your
answer on the space provided.
Equation Equation
1. 9 – 4x = 15 6. s + 15 = - 9
2. x2 -5x + 3 = 0 7. 2x2 + 3x = 8
3. r2 – 144 = 0 8. (w + 3)(w – 4 ) = 4
4. x – 2 = 2x 9. (x + 10)2 = 12
5. 2m(m – 2) = 0 10. x + 12 = 17
II. Write each quadratic equation in standard form, ax2 + bx + c = 0, then identify the values of
a, b, and c.
Equation Standard Form a b C
1. -5 +2x2 = 3x
2. 2x(x + 1) + 8 = 1
3. 2x2 + 3x = - 9
4. (3t + 2)(t + 3) = 8
5. 4x + 5 = - x2
III. Solve the following quadratic equations by extracting square roots, then check.
1. x2 – 225 = -225
Learning Competency
illustrates quadratic equations.
solves quadratic equations by extracting square roots.
2. r2 – 100 = 0
3. (x – 4)2 = 169
4. 2m2 + 10 = 210
End of Quiz No. 1
Quiz No. 2
I. Solve the following quadratic equations by Factoring, then check.
1. x2 +5x+6 = 0
2. t2 + 2t – 19 = 5
II. Solve the following quadratic equations by Completing the Squares, then check.
1. 4m2 – 24m - 108 = 0
Learning Competency
solves quadratic equations by factoring, completing the square and using the
quadratic formula.
2. n2 + 6n + 8 = 0
III. Solve the following quadratic equations by Quadratic Formula, then check.
1. 2m2 + 2m − 12 = 0
2. 5r2 = 80
End of Quiz No. 2
Quiz No. 3
I. Find the value discriminant of each quadratic equation then state the nature of their
roots/solutions.
Equation Discriminant Nature of roots
1. 6p2 − 2p − 3 = 0
2. 5b2 + b − 2 = 0
3. 2p2 + 5p − 4 = 0
4. −2x2 − 8x − 8 = 0
5. −6x2 + 7x + 3 = 0
6. −4m2 − 4m + 5 = 0
7. r2 + 5r + 2 = 0
8. 9n2 − 3n + 2 = 0
9. −7n2 + 8n = 0
10. 4a2 - 8a + 4 = 0
II. Sum and Product of Roots of quadratic Equation.
A. Given the quadratic equations below, find the sum and the product of the roots.
Equation Sum Product
1. x2 + 9x +8 =0
2. 2x2 – 6x – 10 = 0
3. x2 + 9x - 7 =0
4. 3x2 – 3x + 11 = 0
Learning Competency
characterizes the roots of a quadratic equation using the discriminant.
describes the relationship between the coefficients and the roots of a quadratic
equation.
B. Given the roots below, write a quadratic equation with those roots.
Roots Solution Equation
1. 5 and - 2
2. 6 and 3
3. -5 and - 2
4. 2
3 and
1
3
C. Given the sum and the product of the roots, write a quadratic equation.
Sum Product Equation
8 12
-7 -10
5 6
0 -6
End of Quiz No. 3
Quiz No. 4
Transform each of the following equations into a quadratic equation in the form 𝑎𝑥2 +𝑏𝑥 + 𝑐 = 0. 1. 𝑥(𝑥 + 3) = 28
2. 3𝑠(𝑠 − 2) = 12𝑠
3. (𝑡 + 1)2 + (𝑡 − 8)2 = 65
Learning Competency
solves equations transformable to quadratic equations (including rational
algebraic equations
4. 1
𝑥−
𝑥
6=
2
3
5. 2
𝑡−
3𝑡
2= 7
6. 2
𝑟−1+
4
𝑟+5= 7
End of Quiz No. 4
End of Quiz No. 4
Quiz No. 5
Solve the following problems.
1. The length of a rectangle is 5 cm more than its width and the area is 50cm2. Find the length,
width and the perimeter.
2. The length of a rectangular parking is 36 m longer than its width and the area of the parking
lot is 5,152 m2. Find the length, width of the parking lot.
Learning Competency solves problems involving quadratic equations and rational algebraic
equations.
3. The sum of two numbers is 20 and the sum of their square is 232. Find the numbers.
4. The perimeter of a rectangular lot is 44 m and its area is 112 m2. Find the dimension of a
rectangular lot.
End of Quiz No. 5
End of Quiz No. 5
Quiz No. 6
I. Identify which of the following mathematical sentence are quadratic inequalities and not
quadratic inequalities.
1. (x +1) − 4x > 4x − 3 11. m2 − 5m − 14 = 0
2. xy 12. xy
3. 2d2 + 5d ≤ 12 13. 10 − 3x ≤ x2
4. 2x + 5 ≤ x − 3 14. 3x − 2 ≥ x − 6
5. 2x2 ≤ 5x − 2 15. x2 + 9x + 13 > −7
6. b2 − 4b + 4 = 0 16. 2x2 − 3x − 5 = 0
7. b(b + 3) ≥ −2 17. 10 − 9y ≥ −2y2
8. x2 + 4x + 3 = 0 18. 4b2 + 8b + 7 = 4
9. y2 −17y + 70 < 0 19. x(x +1) >112 − 5x
10. 10 − 3x ≤ x2 20. a2 + 25 <10a
II. Find the solution set of each of the following quadratic inequalities.
1. r2 – 10r + 16 < 0
Learning Competency
illustrates quadratic inequalities.
solves quadratic inequalities.
2. m2 – 7m ≤ 10
3. x2 – 5x – 14 > 0
End of Quiz No. 6
Quiz No. 7
I. State whether each of the following equation, table of values and graphs represents a
quadratic functions or not.
1. y = x2 + 2
2. y = 2x +10 3. y = 2x2
4. y = x2 – 1
5. y = x3 + 1
6. y = 2x + 1
7.
x -2 -1 0 1 2
y 0 -3 -4 -3 0
8.
x -2 -1 0 1 2
y -2 0 2 4 6
9.
10.
-5
-4
-3
-2
-1
0
-4 -2 0 2 4
-4
-2
0
2
4
6
8
-4 -2 0 2 4
Learning Competency represents a quadratic function using table of values, graph and equation. transform the quadratic function defined by y = ax2+bx+c into the form
y = a(x - 2)2 + k
II. Transform the quadratic function defined by y = ax2+bx+c into the form y =
a(x - 2)2 + k. 1. y = x2 + 4x +3
2. y = 2x2 – 6x +2
End of Quiz No. 7
End of Quiz No. 7
Quiz No. 8
I. Sketch the graph of each quadratic function quadratic function and identify the vertex,
domain, range and the opening of the graph. State whether the vertex is a minimum or a
maximum point and write the equation of axis of symmetry.
1. y = 2x2 + 4x - 3
2. y = -x2 - 2x - 3
-6
-5
-4
-3
-2
-1
0
1
2
3
4
-4 -3 -2 -1 0 1 2 3 4
-7
-6
-5
-4
-3
-2
-1
0
-4 -3 -2 -1 0 1 2
Learning Competency
graphs a quadratic function: (a) domain; (b) range; (c) intercepts; (d) axis of
symmetry; (e) vertex; (f) direction of the opening of the parabola.
Vertex ________
Opening of the graph: ___________
Vertex is a ________________ point
Equation of the axis of symmetry
_________________
Domain: _________________
Range: _________________
Vertex ________
Opening of the graph: ___________
Vertex is a ________________ point
Equation of the axis of symmetry
_________________
Domain: _________________
Range: _________________
3. y = -2x2 -2
4. y = (x + 2)2 + 3
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 1 2 3 4 5 6
End of Quiz No. 8
0
1
2
3
4
5
6
7
8
-5 -4 -3 -2 -1 0
Vertex ________
Opening of the graph: ___________
Vertex is a ________________ point
Equation of the axis of symmetry
_________________
Domain: _________________
Range: _________________
Vertex ________
Opening of the graph: ___________
Vertex is a ________________ point
Equation of the axis of symmetry
_________________
Domain: _________________
Range: _________________
Quiz No. 9
I. Find the zeros of the following quadratic function if any. Otherwise write none.
Y 𝑓(𝑥) = 4𝑥2 − 25 {−3, −3}
V 𝑓(𝑥) = 9𝑥2 − 16
{2
3,1
2}
G 𝑓(𝑥) = 𝑥2 + 6𝑥 + 9
{−3
2, 1}
U 𝑓(𝑥) = 𝑥2 − 4𝑥 − 21 {5, −4}
S 𝑓(𝑥) = 6𝑥2 + 5𝑥 − 4
{2
3,1
2}
R 𝑓(𝑥) = 𝑥2 − 9
{4
3,4
3}
E 𝑓(𝑥) = 𝑥2 − 5𝑥 − 36 {9, −4}
L 𝑓(𝑥) = 𝑥2 − 𝑥 − 20
{−4
3,1
2}
D 𝑓(𝑥) = 2𝑥2 + 𝑥 − 3
{5
2, −
5
2}
O 𝑓(𝑥) = 6𝑥2 − 7𝑥 + 2
{2
3,1
2}
{7, −3}
II. Determine the quadratic function whose zeroes are given:
_________ 1. 3 and -7
_________ 2. 3 and 2
Learning Competency Find zeros of quadratic functions if any.
determines the equation of a quadratic function given: (a) a table of values;
(b) graph; (c) zeros.
III. Determine the equation of quadratic function described by each graph and table.
_______________ 1.
_______________ 2.
_______________ 3.
x -3 -2 -1 0 1 2
f(x) -22 -9 0 5 6 3
-1
0
1
2
3
-5 -4 -3 -2 -1 0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
-4 -3 -2 -1 0 1 2
End of Quiz No. 9
Summative Test
Direction: Choose the letter that corresponds to your answer.
1. Which of the following quadratic functions has zeros at1 and 5?
a. f(x) = x² - 5x + 6 c. f(x) = x² - 5x -6
b. f(x) = x² - 6x + 5 d. f(x) = x² -6x -5
2. Solve 1
𝑥+2=
𝑥+3
𝑥−1
a. -1, -5 c. 1, 5
b. 5, -1 d. -5 , 1
3. Which of the following is the solution set of (2x+1)² -3 = 6?
a. {2,-1} c. {-2,-1}
b. {-2,1} d. {2, 1 }
4. What number must be added to both sides of x² -4x=7 in order to express the left side as a
square of a binomial?
a. 3 c. 5
b. 4 d. 6
5. The Quadratic Equation whose solutions are 4 and -1/3 is
a. 3x²-11x-4=0 c.3x²+11x-4=0
b. 3x²-x-4=0 d. none of the above
6. Solve 𝑥 − 5 = √𝑥 − 3
a. 5 c. 7
b. 6 d. 8
7. Solve 2
𝑥+
𝑥
2= 2
a. (1,4) c. (2,3)
b. (2,2) d. (3,3)
8. The product of the roots of the equation 𝑚−1
2=
3
𝑚+1 is,
a. -1 c. 3
b. -8 d. 4
9. An object is thrown straight up into the air then follows a trajectory. The height (t) = 80t
-16t². What is the maximum height the object will reach?
a. 20 units c. 50 units
b. 30 units d. 100 units
10. Which is the vertex of the parabola y =3x² - 12 x + 4?
a. (0,0) c. (1,1)
b. (1, -1) d.(2, -8)
11. It is the point of intersection of the axis of symmetry and the parabola. It is also the highest
or lowest point in the graph of a quadratic functions.
a. center c. latus rectum
b. focus d. vertex
12. If x² + mx + 5 = 0 can be solved by factoring and m > 0, m is:
a. 2 c. 5
b. 4 d. 6
13. Which Quadratic function has a graph that opens downward?
a. f(x) = x² c. f(x) = x² - 10 x - 25
b. f(x) = -(X+1)² +4 d. f(x) = 4x²
14. Which of the following has the narrowest graph?
a. f(x) = ½ x² c. f(x) = 2x²
b. f(x) = x² d. f(x) = 4x²
c.
15. Which of the following has the widest graph?
a. f(x) = ½ x² c. f(x) = 2x²
b. f(x) = x² d. f(x) = 4x²
16. What are the dimensions of a 60 – square meter rectangle that can be enclosed by 32 m of
fencing material?
a. 3m by 20m c. 5m by 12 m
b. 4m by 15 m d. 6m by 10 m
17. It is a polynomial equation of degree two that can be written in the form
𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0, where a, b, and c are real numbers and a ≠ 0.
a. Linear Equation c. Quadratic Equation
b. Linear Inequality d. Quadratic Inequality
18. It is a line passing through the vertex of a parabola and divides the parabola into mirror
images.
a. axis of symmetry c. straight line
b. secant line d. tangent line
19. What value of k that will make the trinomial x² -14x + k a perfect square?
a. 25 c. 49
b. 36 d. 64
20. The solution for inequality x² - x -12 < 0 is :
a. -3 < X < -4 c. -3 > X > 4
b. -3 < X < 4 d. 3 < X < 4
Summative Test
Summative Test Cont…
21. What is the vertex form of the quadratic function f(x) = -x² + 2x + 2
a. y = (x – 1)² + 3 c. y = -(x + 1)² - 3
b. y = -(x – 1)² + 3 d. y = (x – 1 ) ² - 3
22. The vertex of the graph of y = x² + 5 is
a. (0,-5) c. (1-5)
b. (0,5) d. none of the above
23. Which of the following mathematical statements is a quadratic inequality?
a. 2r² -3r -5 =0 c. 3t² + 7t -2 ≤ 0
b. 7h +12 < 0 d. s² + 8s + 15 = 0
24. What is the axis of symmetry of y = 3x² - 6x + 12?
a. x = 0 c. x = 4
b. x = 1 d. x = 9
25. The product of the roots of the equation x ( x + 3 ) + 2 = 0 is :
a. 1 c. 3
b. 2 d. 4
26. The graph of a quadratic function is a U – shaped figure called:
a. circle c. hyperbola
b. ellipse d. parabola
27. The following are Quadratic Inequality except for:
a. 3r² + r – 5 ≥ 0 c. 2x² + 5x + 1 > 0
b. s² + 2s + 3 = 0 d. t² + 4t ≤ 10
28. Which among the following values of x will make the inequality x² -4x -12 > 0 true?
a. 0 c. 2
b. 1 d.-3
29. It is a function defined by f(x) = ax² + bx + c, where a,b, and c are real numbers and a ≠ 0.
a. Linear Function c. Mathematical Function
b. Cubic Function d. Quadratic Function
30. The perimeter of a rectangle is 82 m. Its diagonal is 29 m. Find the dimensions of the
rectangle.
a. 15m by 13 m c. 23 m by 18m
b. 21m by 20 m d. 25 m by 20 m
31. The coefficient of the quadratic term in a quadratic equation may be any number
except_________________:
a. 0 c. 3
b. 1 d. 4
32. What is the discriminant of x² - 5x +2 =0
a. 13 c. 17
b. 15 d. 19
33. What is the sum of the roots of 12x² + x = 2?
a. -1/12 c. 2/3
b. 1/2 d. 2
34. What is f(x) = -3(x+2)² + 2 when written in the form f(x) = ax² + bx + c?
a. f(x) = -3x² + 12x -10 c. f(x) = -3x² + 12x + 10
b. f(x) = 3x² - 12x + 10 d. f(x) = -3x² -12x -10
35. A rectangle has a perimeter of 80 cm. If its width is x, its area in terms of x is:
a. A = 40x - x² c. A = x² + 40 x
b. A = 80x + x² d. A = x² + 80 x
36. Which of the following is a solution of 2x²-17x-9=0
a. -1/4 c. 3/8
b. -1/2 d. 1/2
37. Which of the following is a solution of (x-6) (x+5)=12
a. -1/4 c. 7
b. 5 d. 8
38. Which of the following equations has 4 and -9 as the roots?
a. x² - 5x – 36 = 0 c. x² - 5x + 36 = 0
b. x² + 5x – 36 = 0 d. x² + 5x + 36 = 0
39. The equation whose root are twice those of x²-5x+6=0
a. x²-10x-12=0 c. x²-10x+24=0
b. x²-10x+12=0 d. x²+20x+3=0
40. The following equations illustrate a Quadratic Equation except for?
a. m+4=7 c. t²-3t=4
b. 2m(m-4)=3 d.x²+4=0
End of Summative Test
