ACT Math Algebra: Building Skills in Equations, Functions, and Models

Linear equation

An equation whose graph is a straight line; it does not include variables multiplied together, in exponents, or under radicals.

Linear inequality

An inequality that describes a region of values where one linear expression is greater than or less than another.

Slope-intercept form

The line form y = mx + b, where m is the slope and b is the y-intercept.

Standard form

The line form Ax + By = C, usually written with integer coefficients.

Point-slope form

The line form $y - y_1 = m(x - x_1)$, used when a point and a slope are known.

Slope

The rate of change of a line, measured as rise over run: $m = \frac{(y_2 - y_1)}{(x_2 - x_1)}$.

Compound inequality

An inequality chain, such as $2 < 3x + 1 \le 10$, solved by doing the same operations to all three parts.

System of equations

A set of equations that must all be true at the same time.

Substitution

A method for solving a system by replacing one variable with an equivalent expression from another equation.

Elimination

A method for solving a system by adding or subtracting equations to cancel a variable.

Polynomial

An expression made of terms of the form $ax^n$, where $a$ is a constant and $n$ is a nonnegative integer.

Degree

The highest exponent of the variable in a polynomial.

Zero product principle

The rule that if ab = 0, then a = 0 or b = 0.

Quadratic

A polynomial of degree 2, usually written as $ax^2 + bx + c$ with $a$ not equal to 0.

Quadratic formula

The formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, used to solve $ax^2 + bx + c = 0$.

Discriminant

The expression $b^2 - 4ac$ in the quadratic formula; it tells how many real solutions a quadratic has.

Radical expression

An expression that contains a root, such as a square root.

Rational exponent

A fractional exponent, such as $x^{\frac{1}{2}}$, that represents a radical.

Extraneous solution

A value that appears during solving, often after squaring, but does not satisfy the original equation.

Exponential expression

An expression with a variable in the exponent, such as $2^x$.

Growth/decay model

The form $A = A_0(1 + r)^t$, where $A_0$ is the initial amount, $r$ is the rate per period, and $t$ is time.

Function notation

Notation like f(x), which means the output of function f for the input x.

x-intercept

The point where a graph crosses the x-axis; it is found by setting y = 0.

y-intercept

The point where a graph crosses the y-axis; it is found by setting x = 0.

Vertex

The turning point of a parabola; for $y = ax^2 + bx + c$, its x-coordinate is $-b / (2a)$.