Quadratic Equation

Question 1

What is the standard form of a quadratic equation?

Answer 1

ax^2 + bx + c = 0

Question 2

What is the discriminant of a quadratic equation used for?

Answer 2

To determine the nature of the roots

Question 3

What are the types of roots a quadratic equation can have?

Answer 3

Real and distinct, real and equal, complex conjugate

Question 4

What is the formula for finding the roots of a quadratic equation?

Answer 4

x = (-b ± √(b^2 - 4ac)) / 2a

Question 5

True or False: Quadratic equations always have two solutions.

Answer 5

True

Question 6

What is the vertex form of a quadratic equation?

Answer 6

a(x-h)^2 + k

Question 7

What is the relationship between the vertex of a parabola and the coefficient ‘h’ in the vertex form?

Answer 7

The vertex is at (h, k)

Question 8

What does the ‘a’ coefficient in a quadratic equation determine?

Answer 8

The direction and width of the parabola

Question 9

What is the axis of symmetry of a parabola?

Answer 9

A vertical line passing through the vertex

Question 10

What is the formula for finding the vertex of a parabola?

Answer 10

h = -b / 2a, k = f(h)

Question 11

What are the methods for solving a quadratic equation?

Answer 11

Factoring, completing the square, quadratic formula

Question 12

In a quadratic equation, what does it mean if the discriminant is greater than zero?

Answer 12

The equation has two distinct real roots

Question 13

What is the formula for calculating the discriminant of a quadratic equation?

Answer 13

b^2 - 4ac

Question 14

What is the nature of the roots if the discriminant is equal to zero in a quadratic equation?

Answer 14

The equation has two real and equal roots

Question 15

What is the nature of the roots if the discriminant is less than zero in a quadratic equation?

Answer 15

The equation has two complex conjugate roots

Question 16

What is the general form of a quadratic equation?

Answer 16

y = ax^2 + bx + c

Question 17

What is the relationship between the coefficient ‘a’ and the direction of the parabola in a quadratic equation?

Answer 17

Positive ‘a’ opens upwards, negative ‘a’ opens downwards

Question 18

What is the formula for the sum of the roots of a quadratic equation?

Answer 18

-b/a

Question 19

What is the formula for the product of the roots of a quadratic equation?

Answer 19

c/a

Question 20

What is the importance of the discriminant in solving quadratic equations?

Answer 20

It helps determine the number and nature of the roots

Question 21

What is the relationship between the discriminant and the nature of the roots in a quadratic equation?

Answer 21

The discriminant determines whether the roots are real, equal, or complex

Question 22

What is the relationship between the discriminant and the vertex of a parabola?

Answer 22

The discriminant affects the position of the vertex

Question 23

What is the quadratic formula used for?

Answer 23

To find the roots of a quadratic equation

Question 24

What is the difference between linear and quadratic equations?

Answer 24

Quadratic equations have a squared term (ax^2), while linear equations do not