Exam 12/9

Front

What is the definition of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to complete the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, which makes it easier to solve or analyze.

Front

What is the vertex of a parabola represented by the equation f(x) = ax² + bx + c?

Back

The vertex of the parabola can be found using the formula (-b/(2a), f(-b/(2a))). It represents the maximum or minimum point of the function.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression as (x + m)(x + n) where m and n are the found numbers.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.

Front

How do you solve absolute value equations?

Back

To solve an absolute value equation |x - a| = b, set up two equations: x - a = b and x - a = -b, then solve for x.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What does it mean for a function to be undefined?

Back

A function is undefined at a point where it does not have a valid output, often due to division by zero or taking the square root of a negative number.