College Algebra - Homework 7: Quadratic Functions and Inequalities

These flashcards cover key vocabulary terms related to quadratic functions and inequalities as outlined in the College Algebra lecture notes.

Quadratic Function

A polynomial function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Parabola

The graph of a quadratic function, which opens either upward or downward.

Vertex

The highest or lowest point of a parabola, depending on its orientation.

Axis of Symmetry

A vertical line that divides the parabola into two symmetrical halves.

Standard Form

A way to express a quadratic function as f(x) = ax^2 + bx + c.

Vertex Form

A way to express a quadratic function as f(x) = a(x - h)^2 + k, where (h, k) is the vertex.

Maximum

The highest point of a parabola that opens downward.

Minimum

The lowest point of a parabola that opens upward.

X-Intercepts

The points where the parabola crosses the x-axis, also called zeros or roots.

Quadratic Inequality

An inequality that involves a quadratic expression, often represented as ax^2 + bx + c < 0 or > 0.

Completing the Square

A method used to solve quadratic equations by transforming them into a perfect square trinomial.

Quadratic Formula

The solution to the quadratic equation ax^2 + bx + c = 0 given by x = (-b ± √(b² - 4ac))/(2a).

Graphing a Parabola

The process of plotting the points that make up the parabolic curve based on its equation.

Solving Quadratic Word Problems

Applying quadratic equations to real-world situations to find unknown quantities.

Maximum Area Problem

A type of word problem where you find the dimensions that maximize the area of a geometrical shape.