DOL: Quadratic Formula, Complex Number, Solutions, and Absolute

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What are complex numbers?

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit (i = √-1).

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It can be found using the formula (-b/(2a), f(-b/(2a))).

Front

How do you determine the axis of symmetry for a parabola?

Back

The axis of symmetry for a parabola given by the equation y = ax² + bx + c is x = -b/(2a).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, two complex solutions.

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express it in the form (x - p)(x - q) = 0, where p and q are the roots. Then set each factor to zero: x - p = 0 and x - q = 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the range of a quadratic function?

Back

The range of a quadratic function depends on the direction it opens. If it opens upwards, the range is [k, ∞) where k is the minimum value. If it opens downwards, the range is (-∞, k] where k is the maximum value.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value in a quadratic function ax² + bx + c determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.