Formula general de segundo grado Flashcards
(24 cards)
What is the general form of a quadratic equation?
The general form of a quadratic equation is ax² + bx + c = 0.
Identify the coefficients in the quadratic equation 3x² - 5x + 2 = 0.
a = 3, b = -5, c = 2.
True or False: The quadratic formula can be used to find the roots of any quadratic equation.
True.
What is the quadratic formula?
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).
Fill in the blank: The discriminant of a quadratic equation is calculated as _____ .
b² - 4ac.
What does a positive discriminant indicate about the roots of a quadratic equation?
A positive discriminant indicates that there are two distinct real roots.
What does a zero discriminant indicate about the roots of a quadratic equation?
A zero discriminant indicates that there is exactly one real root (a repeated root).
What does a negative discriminant indicate about the roots of a quadratic equation?
A negative discriminant indicates that there are no real roots, only complex roots.
If a = 1, b = 2, and c = 1, what are the roots of the equation x² + 2x + 1 = 0?
The roots are x = -1 (a repeated root).
True or False: The roots of the equation 2x² + 4x + 2 = 0 can be simplified.
True.
Use the quadratic formula to solve for x: 2x² + 3x - 2 = 0.
The roots are x = 0.5 and x = -2.
What is the vertex form of a quadratic equation?
The vertex form is y = a(x - h)² + k, where (h, k) is the vertex.
Identify the vertex of the quadratic function y = 2(x - 1)² + 3.
The vertex is (1, 3).
How can you find the axis of symmetry for a quadratic equation?
The axis of symmetry can be found using the formula x = -b / (2a).
What is the axis of symmetry for the equation x² - 4x + 6 = 0?
The axis of symmetry is x = 2.
Fill in the blank: The maximum or minimum value of a quadratic function occurs at the _____ .
vertex.
What is the maximum value of the quadratic function y = -3x² + 6x + 1?
The maximum value is 7, occurring at x = 1.
True or False: Every quadratic function has at least one real root.
False.
How do you determine if a quadratic equation opens upwards or downwards?
If a > 0, it opens upwards; if a < 0, it opens downwards.
What is the solution of the quadratic equation x² - 5x + 6 = 0?
The solutions are x = 2 and x = 3.
What is the sum of the roots of the quadratic equation ax² + bx + c = 0?
The sum of the roots is -b/a.
What is the product of the roots of the quadratic equation ax² + bx + c = 0?
The product of the roots is c/a.
Use the quadratic formula to solve for x: 5x² - 20 = 0.
The roots are x = 2 and x = -2.
What is the significance of the vertex in a quadratic function?
The vertex represents the highest or lowest point of the parabola.
