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 form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form ax² + bx + c is given by the formula 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 range of a quadratic function that opens upwards?

Back

The range of a quadratic function that opens upwards is [k, ∞), where k is the minimum value of the function.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a quadratic function that opens downwards is (-∞, k], where k is the maximum value of the function.

Front

How do you find the solutions of a quadratic equation using factoring?

Back

To find the solutions using factoring, rewrite the quadratic equation 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 an absolute value function?

Back

An absolute value function is a function that outputs the non-negative value of its input, defined as f(x) = |x|. It reflects negative values across the x-axis.

Front

How do you find the range of an absolute value function?

Back

To find the range of an absolute value function of the form f(x) = |ax + b| + c, identify the minimum value of the function, which is c, and the range is [c, ∞).