Tap or click on cards to flip them and reveal the answers. You can use arrow keys as well.
Loading folders...
1/15 cards
What is a quadratic equation?
Click to flip
A quadratic equation is a polynomial equation of degree 2, typically in the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
Click to flip
What is the standard form of a quadratic equation?
Click to flip
The standard form of a quadratic equation is ax^2 + bx + c = 0.
Click to flip
What does 'a' represent in a quadratic equation?
Click to flip
In a quadratic equation, 'a' is the coefficient of x^2 and it determines the parabola's direction (upwards if a > 0, downwards if a < 0).
Click to flip
How do you find the solutions to a quadratic equation?
Click to flip
Solutions can be found using the quadratic formula, factoring, or completing the square.
Click to flip
What is the quadratic formula?
Click to flip
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).
Click to flip
What does the discriminant in a quadratic equation tell us?
Click to flip
The discriminant (b^2 - 4ac) indicates the nature of solutions: if positive, two real solutions; if zero, one real solution; if negative, no real solution.
Click to flip
When is a quadratic equation considered to be in vertex form?
Click to flip
A quadratic equation is in vertex form when it is written as y = a(x-h)^2 + k, where (h, k) is the vertex.
Click to flip
What is the role of the coefficient 'b' in the quadratic equation?
Click to flip
The coefficient 'b' affects the position and direction of the graph, impacting the axis of symmetry and vertex.
Click to flip
What is factoring in terms of solving quadratic equations?
Click to flip
Factoring involves expressing the quadratic equation as a product of binomial expressions, used to find its solutions.
Click to flip
How do you complete the square for a quadratic equation?
Click to flip
Completing the square involves rewriting the quadratic in the form (x + p)^2 = q, enabling easier solving.
Click to flip
What is the axis of symmetry in a quadratic equation?
Click to flip
The axis of symmetry of a quadratic function is the vertical line x = -b/(2a).
Click to flip
What is a real-world example of a quadratic relationship?
Click to flip
Projectile motion, where the trajectory of an object can be described by a quadratic equation.
Click to flip
What shapes do the graphs of quadratic equations form?
Click to flip
The graphs of quadratic equations are parabolas.
Click to flip
Can quadratic equations have complex solutions?
Click to flip
Yes, if the discriminant is negative, the solutions are complex (not real).
Click to flip
What determines the width of the parabola in a quadratic equation?
Click to flip
The value of 'a' affects the width; larger absolute values of 'a' make the parabola narrower, smaller values make it wider.
Click to flip
Need More Study Materials?
Go back to the chat to generate additional resources.