#1
Which of the following represents a quadratic equation?
y = 3x - 7
y = x^2 + 5x + 6
y = 2x + 4
y = 4x - 3
#2
What does the term 'quadratic' refer to in quadratic equations?
The highest power of the variable is 2
The equation involves two variables
The equation is solved using two methods
The equation has two distinct roots
#3
Which of the following is a characteristic feature of the graph of a quadratic function?
A straight line
A curve
A loop
A staircase pattern
#4
What is the standard form of a quadratic equation?
y = ax^2 + bx + c
y = a(x - h)^2 + k
y = (x - h)(x - k)
y = a(x + h)^2 + k
#5
Which of the following is a quadratic function?
f(x) = 2x - 3
f(x) = √x
f(x) = x^3
f(x) = 3x^2 - 5x + 2
#6
What is the term used to describe the highest or lowest point on the graph of a quadratic function?
Root
Axis of symmetry
Vertex
Discriminant
#7
What is the formula to find the roots of a quadratic equation ax^2 + bx + c = 0?
(-b ± √(b^2 - 4ac)) / (2a)
(-b ∓ √(b^2 - 4ac)) / (2a)
(-b ∓ √(4ac - b^2)) / (2a)
(b ± √(b^2 - 4ac)) / (2a)
#8
In a real-world context, which scenario can be modeled using a quadratic equation?
The temperature of a room over time
The distance traveled by a car with constant speed
The trajectory of a ball thrown in the air
The annual income of a company
#9
What does the discriminant of a quadratic equation determine?
The number of real roots
The sum of the roots
The nature of the roots
The product of the roots
#10
Which method can be used to solve a quadratic equation when factoring is not possible?
Completing the square
Guess and check
Trial and error
Long division
#11
What is the vertex form of a quadratic equation?
y = ax^2 + bx + c
y = a(x - h)^2 + k
y = (x - h)(x - k)
y = a(x + h)^2 + k
#12
Which of the following statements about the axis of symmetry of a quadratic function is true?
It is always parallel to the y-axis
It divides the parabola into two equal halves
It is always parallel to the x-axis
It intersects the vertex of the parabola
#13
In the quadratic equation ax^2 + bx + c = 0, if the discriminant is negative, what can we conclude about the roots?
The roots are real and distinct
The roots are real and equal
The roots are imaginary
The roots cannot be determined
#14
If a quadratic equation has one real root and one imaginary root, what can be said about its discriminant?
The discriminant is negative
The discriminant is zero
The discriminant is positive
The discriminant is not applicable
#15
If a quadratic equation has a negative discriminant, what can be concluded about the roots?
The roots are real and equal
The roots are real and distinct
The roots are imaginary
The nature of the roots cannot be determined
#16
If the discriminant of a quadratic equation is zero, what can be concluded about its roots?
The equation has two distinct real roots.
The equation has two real roots, which are equal.
The equation has no real roots.
The nature of the roots cannot be determined.
#17
For a quadratic function f(x) = ax^2 + bx + c, if a > 0, what can be said about the vertex of the parabola?
The vertex is a maximum point.
The vertex is a minimum point.
The vertex lies in the third quadrant.
The vertex lies on the x-axis.