Math Pre Calculus 107 Test 1

Quadratic Equation

An equation in the form ax² + bx + c = 0.

Factoring

Expressing the quadratic as a product of linear factors.

Square Root Method

Solving quadratic equations in the form x² = k or (x-h)² = k by taking square roots.

Completing the Square

Transforming a quadratic equation into the form (x-h)² = k by adding (b/2a)² to both sides.

Quadratic Formula

A method for solving any quadratic equation, given by x = (-b ± √(b² - 4ac)) / (2a).

Complex Number

A number of the form z = a + bi, where a is the real part and b is the imaginary part.

Imaginary Unit i

Defined as √(-1), with properties such that i² = -1.

Conjugate of a Complex Number

The conjugate of z = a + bi is z̅ = a - bi.

Rational Equation

An equation that contains fractions with polynomials in the numerator or denominator.

Radical Equation

An equation that contains a variable under a radical (square root, cube root, etc.).

Linear Inequality

An inequality that can be expressed in linear form (ax + b < 0, ax + b ≥ 0, etc.).

Absolute Value

The distance of a number from zero on the number line, denoted |u|.

Midpoint Formula

The midpoint M of a line segment joining (x₁, y₁) and (x₂, y₂) is M = ((x₁+x₂)/2, (y₁+y₂)/2).

Distance Formula

The distance d between two points (x₁, y₁) and (x₂, y₂) is given by d = √((x₂ - x₁)² + (y₂ - y₁)²).

Symmetry with respect to the y-axis

If replacing x with -x in the equation yields an equivalent equation.

Standard Form of a Circle

The equation of a circle is (x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius.

Intercepts of a Graph

Points where the graph intersects the x-axis (x-intercept) or y-axis (y-intercept).

Compound Inequality

Inequalities that involve two separate inequalities, connected by 'and' or 'or'.