Algebra: Quadratic Formula and Word Problems Review

Flashcards covering key vocabulary and concepts related to quadratics, their properties, and related word problems.

Discriminant

A value that determines the number and type of roots of a quadratic equation, calculated as $b^2 - 4ac$.

Quadratic Formula

A formula used to find the roots of a quadratic equation given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Rational Roots Theorem

If a polynomial has rational roots, they can be expressed as the ratio of factors of the constant term to factors of the leading coefficient.

Area of a Rectangle

Given by the formula $A = l \times w$, where $l$ is length and $w$ is width.

Turning Point (Vertex)

The highest or lowest point on the graph of a parabola, found at $x = -\frac{b}{2a}$ for the equation $y = ax^2 + bx + c$.

Axis of Symmetry

A vertical line that divides the parabola into two mirror-image halves, given by the line $x = -\frac{b}{2a}$.

Consecutive Integers

Two integers that follow one after another, such as $n$ and $n+1$.

Roots of a Quadratic Equation

The values of $x$ for which the equation $ax^2 + bx + c = 0$ is satisfied.

Area of a Triangle

Given by the formula $A = \frac{1}{2} \times base \times height$.

Quadratic-Linear Pair

A system of equations where one is quadratic and the other is linear, often requiring special methods for solving.