Quadratic Formula Flashcards
Remeber the QF (18 cards)
What is the standard form of a quadratic equation?
ax^2 + bx + c = 0
What does ‘a’ represent in the quadratic equation?
‘a’ represents the coefficient of x^2.
What is the quadratic formula used to find?
The roots or solutions of a quadratic equation.
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / (2a)
True or False: The quadratic formula can only be used for equations where a ≠ 0.
True
In the quadratic formula, what does the term ‘b² - 4ac’ represent?
The discriminant of the quadratic equation.
What does a positive discriminant indicate?
Two distinct real roots.
What does a discriminant of zero indicate?
One real root (a repeated or double root).
What does a negative discriminant indicate?
No real roots (two complex roots).
Fill in the blank: The quadratic formula is derived from completing the __________.
square
If a = 1, b = -3, and c = 2, what are the roots of the equation using the quadratic formula?
x = 1 and x = 2
True or False: The quadratic formula can be used for any polynomial equation.
False
If a quadratic equation has roots p and q, what is the factored form of the equation?
a(x - p)(x - q) = 0
What is the relationship between the roots and coefficients of a quadratic equation?
p + q = -b/a and pq = c/a
What does the term ‘roots’ refer to in the context of quadratics?
The values of x that make the quadratic equation equal to zero.
True or False: Quadratic equations can have at most two real solutions.
True
What is the first step in using the quadratic formula?
Identify the coefficients a, b, and c from the equation.
How can the quadratic formula be derived?
By completing the square on the general form of the quadratic equation.
