Pre-Calculus (Algebra 2) Test Review

Distance Formula

• Formula for determining the distance between two points ((x_1, y_1)) and ((x_2, y_2)) is given by (d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2})

Midpoint Formula

• To find the midpoint between two points ((x_1, y_1)) and ((x_2, y_2)), use the formula ((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}))

Quadratic Formula

• The quadratic formula to solve equations of the form (ax^2 + bx + c = 0) is (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a})

Circle Formula

• The equation of a circle with center ((h, k)) and radius (r) is given by ((x - h)^2 + (y - k)^2 = r^2)

Slope Formula

• The slope (m) between two points ((x_1, y_1)) and ((x_2, y_2)) is calculated as (m = \frac{y_2 - y_1}{x_2 - x_1})

Slope Intercept Formula

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

Slope Standard Form

• A linear equation can also be expressed in standard form as (Ax + By = C), where (A), (B), and (C) are integers, and (A) is non-negative

Discriminant

• The discriminant of a quadratic (ax^2 + bx + c) is calculated using (D = b^2 - 4ac) to help determine the nature of the roots

Discriminant > 0

• If (D > 0), the quadratic equation has two distinct real solutions

Discriminant < 0

• If (D < 0), the quadratic equation has no real solutions, indicating complex roots

Discriminant = 0

• If (D = 0), the quadratic equation has exactly one solution (or a repeated solution) which means the vertex touches the x-axis