Question 1

Which of the following illustrates a quadratic equation?

Accepted Answer

2x – x² = 9

Answer

x + 5 = 0

Answer

7 – 4x > x²

Answer

6x² + 18 – 12x

Question 2

What will happen if a = 0 in the standard form of quadratic equation, 𝑎𝑥²+ bx + c = 0 ?

Accepted Answer

The equation becomes linear.

Answer

The equation is still quadratic.

Answer

The degree of the equation remains 2.

Answer

The equation becomes an inequality.

Question 3

Determine the solution set of 𝑥² - 144 = 0 using extracting the square roots.

Accepted Answer

{12, -12}

Answer

√144

Answer

x2= 144

Answer

144

Question 4

What values of x will make the quadratic equation 3𝑥²= 75 TRUE?

Accepted Answer

<math>\pm</math> 5

Answer

225

Answer

<math>\pm</math>  25

Answer

72

Question 5

Which of the following are the factors of the quadratic equation x²- 12x + 20 = 0?

Accepted Answer

(x - 10) (x - 2)

Answer

(x - 1) (x - 20)

Answer

(x +12) (x + 20)

Answer

(x - 4) (x - 5)

Question 6

Determine the positive root of the quadratic equation x²+ 5x - 6 = 0.

Accepted Answer

1

Answer

11

Answer

6

Answer

-30

Question 7

To solve by completing the square, what would be the constant term in the quadratic equation x²- 5x + _____ = 0?

Accepted Answer

25/4

Answer

1/2

Answer

5/2

Answer

25

Question 8

In the process of completing the square, what must be the initial step if the first term has acoefficient greater than one?

Accepted Answer

Divide both sides by this coefficient

Answer

Multiply all terms by zero

Answer

Move it to the other side

Answer

Multiply both sides by this coefficient

Question 9

What is the quadratic formula?

Accepted Answer

Answer

ax²+ bx + c = 0

Answer

b2 - 4ac

Answer

$\left(\frac{b}{2}\right)^2$

Question 10

Using quadratic formula, what are the roots of 𝑥²+ 15 =− 8 ?

Accepted Answer

{-3, -5}

Answer

{7, -7}

Answer

{23, -23}

Answer

{-1, -15}

Question 11

The nature of the roots depends on the value b² − 4ac and it is known as the ______.

Accepted Answer

discriminant

Answer

quadratic formula

Answer

quadratic equation

Answer

standard form

Question 12

Describe the discriminant and nature of the roots of 3x² + 5x - 2 = 0.

Accepted Answer

The discriminant is greater than 0 and is a perfect square, the two roots are real andrational.

Answer

The discriminant has two real roots.

Answer

The discriminant has no real roots.

Answer

The discriminant is greater than 0 and is not a perfect square, the two roots are real and irrational.

Question 13

In the quadratic equation 3𝑥²- 5x + 4 = 0, what is the sum of its roots?

Accepted Answer

5/3

Answer

4/3

Answer

-8

Answer

12

Question 14

Solve for the sum and product of the roots of the quadratic equation 2x² + 7x - 5 = 0.

Accepted Answer

Sum =-7/2, Product =-5/2

Answer

Sum = 9, Product = -10

Answer

B. Sum =5/2 , Product = 7/2

Answer

Sum = 4, Product = - 70

Question 15

Which equation has roots whose sum is -7 and whose product is -10?

Accepted Answer

x² + 7x - 10 = 0

Answer

x²- 2x - 5 = 0

Answer

x²- 17x + 70 = 0

Answer

x²- 3x - 5 = 0

Question 16

Which quadratic equation is equivalent to $\frac{x\ +\ 3}{5}=\ \frac{2}{x}$ ?

Accepted Answer

x²+ 3x - 10 = 0

Answer

x - 10 = 0

Answer

2x + 6 = 5x

Answer

x² + 3x = 10

Question 17

What are the factors of the quadratic equation x²- 3x + 2 = 0 ?

Accepted Answer

(𝑥 − 1)(𝑥 − 2)

Answer

(𝑥 + 1)(𝑥 − 3) B. 2)

Answer

(𝑥 − 3)(𝑥 +2)

Answer

x² - 3x = -2

Question 18

Express (𝑥 − 4)² = 15 in standard form.

Accepted Answer

x²- 8x + 1 = 0

Answer

x²- 19 = 0

Answer

x²- 8x + 31 = 0

Answer

(𝑥 − 4)²- 15 = 0

Question 19

Determine the roots of the quadratic equation formed in (𝑥 − 4)² = 15. (refer to #18)

Accepted Answer

x = 4

\left(\frac{b}{2}\right)^2

Answer

x = ± 19

Answer

x - 4 = ±

\left(\frac{b}{2}\right)^2

Answer

<math>\surd\left(x-4\right)^2\ =\pm\surd15</math>

Question 20

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

Accepted Answer

Answer

Answer

$\left(\frac{b}{2}\right)^2$

Answer

Question 21

Find two consecutive integers whose product is 90.

Accepted Answer

9 and 10

Answer

5 and 8

Answer

1 and 90

Answer

2 and 45

Question 22

The height of a triangle is 4m greater than twice its base. The area of the triangle is 168𝑚² . Represent the area of the triangle?

Accepted Answer

<math>\frac{x\left(2x+4\right)}{2}=\ 168</math>

Answer

12m

Answer

14m

Answer

x(2x+4)=168

Question 23

A motorboat whose speed is 9 kph in still water goes 12 km downstream and comes back in a total time of 3 hours. Which of the following rational equations is appropriate in solving the problem?

Accepted Answer

Answer

12(9-x) + 12(9+x) = 3

Answer

3 + 9 = 12

Answer

12 - 9 = 3

Question 24

The product of the digits of a two-digit number is 20. If 9 is subtracted from the number, the digits are interchanged. Find the original number.

Accepted Answer

54

Answer

45

Answer

20

Answer

29

Question 25

What is the mathematical translation of the symbol for “square of x is subtracted by half of x is greater than 0”?

Accepted Answer

Answer

Answer

Answer

$\left(\frac{b}{2}\right)^2$

Question 26

All of these are inequalities in one variable EXCEPT _______.

Accepted Answer

𝑥 ²+ 𝑦 − 6 > -1

Answer

− 6 − 10𝑥 ² ≥ − 1

Answer

5𝑡² − 25 < 3t

Answer

− 5𝑟²+ 𝑟 ≤ 0

Question 27

Which of the following is the solution set of 𝑡²- 6 < t?

Accepted Answer

(-2, 3)

Answer

(6,-1)

Answer

(𝑡 − 3)(𝑡 + 2)

Answer

0

Question 28

Find the solution for 2𝑡²+11t+12<0.

Accepted Answer

− 4 < 𝑥 <−

\left(\frac{b}{2}\right)^2

Answer

(𝑡 + 4)(2𝑡 + 3)

Answer

$\left(\frac{b}{2}\right)^2$

Answer

<math>\left\{-4,-\frac{3}{2}\right\}</math>

Question 29

Which of the following is the correct mathematical translation to the verbal statement“ Five times the result of ten added to a number is greater than nine”?

Accepted Answer

5(10 + x) > 9

Answer

4x + 10x > 9

Answer

5(x + 10) < 9

Answer

4x + x > 9

Question 30

How do we translate the verbal sentence, “the length is at most twelve inches” into a mathematical sentence?

Accepted Answer

/ ≥ 12

Answer

/ = 12

Answer

/ > 12

Answer

/ ≤ 12

Question 31

Which situation models quadratic function?

Accepted Answer

throwing a ball upward

Answer

path of a launching airplane

Answer

throwing a ball downward

Answer

track of a jet

Question 32

What do you call the graph of a quadratic function?

Accepted Answer

Parabola

Answer

Ellipse

Answer

Line

Answer

Hyperbola

Question 33

How do you know if the table of values is a quadratic function or not?

Accepted Answer

If the second differences in y are equal.

Answer

If the first differences in y are equal.

Answer

If the values of y are all positive.

Answer

None of the above.

Question 34

Which table of values represents a quadratic function?

Accepted Answer

A.

Answer

B.

Answer

C.

Answer

D.

Question 35

Which is the graph of a quadratic function?

Accepted Answer

D.

Answer

A.

Answer

B.

Answer

C.

Question 36

Which equation represents a quadratic function?

Accepted Answer

<math>f\left(x\right)\ =\ x^2\ +\ 3x</math>

Answer

Answer

$\left(\frac{b}{2}\right)^2$

Answer

<math>f\left(x\right)=2\ -\ x\ \left(4-x\right)</math>

Question 37

What is the vertex form of 𝑓(𝑥) = 𝑥²- 8x + 17?

Accepted Answer

<math>f\left(x\right)\ =\ \left(x-4\right)^2+1</math>

Answer

$\left(\frac{b}{2}\right)^2$

Answer

<math>f\left(x\right)=\left(x-4\right)^2</math>

Answer

<math>f\left(x\right)=\ x^2-8x+16+17+16</math>

Question 38

Which is the general form of the quadratic function 𝑓(𝑥) = 2(𝑥 − 2²) - 3?

Accepted Answer

f(x) = 2𝑥² − 8x + 5

Answer

f(x) = 2(𝑥² − 4x + 4) − 3

Answer

𝑓(𝑥) =2x²− 8x + 8 - 3

Answer

𝑓(𝑥) = (𝑥² − 4𝑥 + 4) − 6

Question 39

What function will be obtained if y = 2𝑥² will be moved 3 units to the left and 5 upward?

Accepted Answer

y = 2 (x+3)² + 5

Answer

y = 2𝑥² + 3 + 5

Answer

y = 𝑥² + 8

Answer

y =2(𝑥² + 3)²

Question 40

The highest or lowest point of a parabola is called _________

Accepted Answer

vertex

Answer

range

Answer

domain

Answer

symmetry

Question 41

Describe the graph of 𝑓(𝑥) = (𝑥 + 2)²+3 ?

Accepted Answer

y

\left(\frac{b}{2}\right)^2

3

Answer

The graph opens upward.

Answer

𝑦 ≤ 3.

Answer

The graph opens downward.

Question 42

If the vertex of the graph is (5, -7), what is its axis of symmetry?

Accepted Answer

x = 5

Answer

x = -5

Answer

0

Answer

-2

Question 43

How do you sketch the graph of 𝑦 = 𝑎(𝑥 − ℎ)² , based on the graph of 𝑦 = 𝑎𝑥².

Accepted Answer

horizontally

Answer

diagonally

Answer

vertically

Answer

wriggly

Question 44

In 𝑓(𝑥) = 𝑎(𝑥 − ℎ)² , what will happen to the parabola if we increase the value of k?

Accepted Answer

The parabola will move downward.

Answer

The parabola will move.

Answer

The parabola will move to the left.

Answer

The parabola will move upward

Question 45

How will the graph of 𝑓(𝑥) = (𝑥 + 1)²- 2being obtained by sliding the graph of y = x²?

Accepted Answer

Slide 1 unit to the left and 2 units downward

Answer

Slide 1 unit to the right and 2 units downward

Answer

Slide to the right and slide upward

Answer

Slide 1 unit to the left

Question 46

What is the quadratic function that represents this table of values?

Accepted Answer

<math>f\left(x\right)=x^2+3x-5</math>

Answer

<math>f\left(x\right)=x^2-2x+5</math>

Answer

<math>f\left(x\right)=x^2\ +\ 3x-4-1</math>

Answer

$\left(\frac{b}{2}\right)^2$

Question 47

Given the zeroes of a quadratic function which are -8 and − 5. What is the equation of thequadratic function?

Accepted Answer

𝑓(𝑥) = 𝑥²+ 13𝑥 + 40

Answer

𝑓(𝑥) = (𝑥 + 8)(𝑥 + 5)

Answer

𝑓(𝑥) = 𝑥² − 8𝑥 − 5

Answer

𝑓(𝑥) = (𝑥 − 8)(𝑥 − 5)

Question 48

What is the equation given the graph of a function at the right.

Accepted Answer

𝑓(𝑥) = − 5𝑥²+ 1

Answer

𝑓(𝑥) = 5x + 1

Answer

𝑓(𝑥) = − (5𝑥² − 1)

Answer

𝑓(𝑥) = 5𝑥²− 1

Question 49

A rifle bullet is fired vertically upward. Its height in feet t seconds later is given by ℎ(𝑡) = 960𝑡 − 16𝑡² . What is the maximum height attained by the bullet?

Accepted Answer

14, 400 ft

Answer

144 ft

Answer

40, 140 ft

Answer

14, 440 ft

Question 50

The profit P(x) of a shoe company is represented by 𝑃(𝑥) = 2𝑥²-80𝑥 + 1500 , where x is number of shoes sold. What is the company’s profit if there are 50 pairs of shoes sold? Write an equation for the revenue function.

Accepted Answer

₱ 2,500

Answer

₱ 1,170

Answer

₱ 1,210

Answer

₱ 1,300

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