Quadratic Equation Flashcards
What is the standard form of a quadratic equation?
ax^2 + bx + c = 0
What is the discriminant of a quadratic equation used for?
To determine the nature of the roots
What are the types of roots a quadratic equation can have?
Real and distinct, real and equal, complex conjugate
What is the formula for finding the roots of a quadratic equation?
x = (-b ± √(b^2 - 4ac)) / 2a
True or False: Quadratic equations always have two solutions.
True
What is the vertex form of a quadratic equation?
a(x-h)^2 + k
What is the relationship between the vertex of a parabola and the coefficient ‘h’ in the vertex form?
The vertex is at (h, k)
What does the ‘a’ coefficient in a quadratic equation determine?
The direction and width of the parabola
What is the axis of symmetry of a parabola?
A vertical line passing through the vertex
What is the formula for finding the vertex of a parabola?
h = -b / 2a, k = f(h)
What are the methods for solving a quadratic equation?
Factoring, completing the square, quadratic formula
In a quadratic equation, what does it mean if the discriminant is greater than zero?
The equation has two distinct real roots
What is the formula for calculating the discriminant of a quadratic equation?
b^2 - 4ac
What is the nature of the roots if the discriminant is equal to zero in a quadratic equation?
The equation has two real and equal roots
What is the nature of the roots if the discriminant is less than zero in a quadratic equation?
The equation has two complex conjugate roots
What is the general form of a quadratic equation?
y = ax^2 + bx + c
What is the relationship between the coefficient ‘a’ and the direction of the parabola in a quadratic equation?
Positive ‘a’ opens upwards, negative ‘a’ opens downwards
What is the formula for the sum of the roots of a quadratic equation?
-b/a
What is the formula for the product of the roots of a quadratic equation?
c/a
What is the importance of the discriminant in solving quadratic equations?
It helps determine the number and nature of the roots
What is the relationship between the discriminant and the nature of the roots in a quadratic equation?
The discriminant determines whether the roots are real, equal, or complex
What is the relationship between the discriminant and the vertex of a parabola?
The discriminant affects the position of the vertex
What is the quadratic formula used for?
To find the roots of a quadratic equation
What is the difference between linear and quadratic equations?
Quadratic equations have a squared term (ax^2), while linear equations do not
