Lesson 76: Finding Roots of Quadratic Equations

This set of flashcards covers vocabulary and key concepts from Lesson 76 of ShoreMont Mathematics Algebra one, focusing on finding the roots and zeros of quadratic equations.

ShoreMont Mathematics Algebra one

The specific course name for which Lesson 76 serves as the first lesson of the final quarter, consisting of 25 lessons.

Standard form of a quadratic equation

The expression represented by $ax^2 + bx + c = 0$.

Root of a polynomial

The value of $x$ when $y$ or $f(x)$ equals $0$; used interchangeably with the term "zero".

Zero

A synonym for the root of a polynomial used when setting binomials equal to zero to solve for $x$.

Zero factor theorem

A rule stating that if $a$ and $b$ are real numbers such that $a \times b = 0$, then either $a = 0$, $b = 0$, or both are zero.

Parabola

The geometric shape formed when graphing quadratic equations of the form $y = ax^2 + bx + c$ on an $x y$ axis.

Mathematics

Described as the "language of science" and a tool for studying God’s creation.

Acceleration

A specific type of motion that serves as a real-world application for quadratic equations.

Binomial

The factorable parts of a trinomial, such as $(x + 3)$ and $(x + 2)$, where the order of multiplication does not matter.

Opposite of the constant

A mental method for finding roots where the value of $x$ is the negative of the constant term in a factored binomial (e.g., if the constant is $3$, then $x = -3$).

Quadratic relationship

A pattern that can be factored into binomials even in non-quadratic equations, such as after factoring an $x$ out of $x^3 - 6x^2 + 8x = 0$.