Algebra: Quadratic Formula and Word Problems Review

Flashcards covering key algebra vocabulary related to quadratic formulas, equations, and word problems.

Discriminant

A value used to determine the nature of the roots of a quadratic equation.

Quadratic Formula

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

Roots

The solutions of a quadratic equation.

Rational Roots

Roots of a polynomial that can be expressed as the quotient of two integers.

Irrational Roots

Roots that cannot be expressed as a quotient of two integers.

Area of Rectangle

The product of its length and width.

Quadratic Linear Pair

A pair of equations consisting of a quadratic equation and a linear equation.

Turning Point

The vertex of a parabola represented in a quadratic equation.

Axis of Symmetry

A vertical line that divides a parabola into two mirror-image halves.

Quadratic Word Problem

A real-world scenario that can be represented with a quadratic equation.

Completing the Square

A method used to convert a quadratic equation into a perfect square trinomial.

Vertex Form of a Quadratic

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

Area of Triangle

Calculated as $A = \frac{1}{2} \times base \times height$.

Quadratic Function

A function that can be described by a quadratic equation of the form $y = ax^2 + bx + c$.

Simultaneous Equations

A set of equations with multiple variables that can be solved together.

Sum of Roots

The total value obtained when two roots of a quadratic equation are added; given by $-\frac{b}{a}$.

Product of Roots

The value obtained when two roots of a quadratic equation are multiplied; given by $\frac{c}{a}$.

Linear Equation

An equation that represents a straight line, typically in the form $y = mx + b$.

System of Equations

A set of equations with the same variables.

Consecutive Integers

Integers that follow each other in order; for example, 3 and 4.

Right Triangle

A triangle with one angle measuring 90 degrees.

Dimensions of a Rectangle

The measurements of length and width.

Ratio

A relationship between two quantities, indicating how many times one value contains or is contained within the other.

Height of a Triangle

The perpendicular distance from the base to the opposite vertex.

Base of a Triangle

One side of a triangle, often used as a reference for the height.

Equation of a Parabola

Mathematical expression describing the shape and location of a parabola, typically in the form $y = ax^2 + bx + c$.

Quadratic Equation

An equation that can be rearranged in the standard form $ax^2 + bx + c = 0$.

Systems of Linear Equations

Equations that can be represented as lines on a graph.

Negative Discriminant

Indicates that there are no real roots, only complex roots.

Positive Discriminant

Indicates that there are two distinct real roots.

Zero Discriminant

Indicates that there is exactly one real root, or a repeated root.

Parabola

A U-shaped graph that represents a quadratic function.

Quadratic Terms

Terms in a polynomial equation where the variable is raised to the second power.

Conjugate Roots

Roots that are in the form of a complex number when they cannot be simplified to rational numbers.

Area of a Rectangle Equation

If width is $w$ and length is $l$, then the area is given by: $A = l \times w$.

Real Numbers

Any value that can be found on the number line.

Factors of Quadratics

Values that multiply together to give the quadratic equation.

Root Finding Methods

Techniques used to determine the solutions (roots) of a quadratic equation.

Substitution Method

A method for solving equations by substituting one variable with another variable.

Quadratic Models

Mathematical models that use quadratic equations to represent phenomena.

Graph of a Quadratic

A visual representation of all the solutions to a quadratic equation.

Inequalities

Mathematical expressions indicating the range of values that satisfy a condition.

Parameter

A variable that defines a system or a set of equations.

Inequalities in Quadratics

Expressions that compare quadratic expressions instead of equations.

Real World Applications

Practical uses of quadratic equations in different fields.

Graphical Representation

Using graphs to showcase mathematical relationships or data.

Leg Lengths of Right Triangle

Lengths of the two sides that form the right angle in a right triangle.

Length of Rectangle

The longer side of a rectangle, often symbolized by $l$.

Width of Rectangle

The shorter side of a rectangle, often symbolized by $w$.

Method of Elimination

A technique for solving systems of equations by eliminating a variable.

Consecutive Positive Integers Problem

Finding two positive integers that follow each other and meet certain conditions.