Linear Equations & Absolute Value Equations & Quadratics

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = 0, where a and b are constants.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, where p and q are the roots. Then, set each factor equal to zero and solve for x.

Front

What does the ± symbol represent in quadratic equations?

Back

The ± symbol indicates that there are two possible solutions when taking the square root of both sides of an equation.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots: if positive, two real solutions; if zero, one real solution; if negative, no real solutions.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, set up two separate equations: one for the positive case and one for the negative case, then solve each equation.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the process for completing the square?

Back

Completing the square involves rewriting a quadratic in the form (x - p)² = q, allowing for easier solving and graphing.

Front

What is a solution to a system of linear equations?

Back

A solution to a system of linear equations is a set of values that satisfy all equations in the system simultaneously.