Questions and Answers
What is the formula used to calculate the distance between two points?
Which formula is used to find the midpoint of a line segment?
What is the formula for solving quadratic equations?
Which of the following is the formula representing a circle?
Signup and view all the answers
What is the formula used to find the slope of a line?
Signup and view all the answers
What is the slope-intercept formula for the equation of a line?
Signup and view all the answers
What is the standard form of a linear equation?
Signup and view all the answers
What is the discriminant of a quadratic equation?
Signup and view all the answers
If the discriminant is greater than 0, you will have 1 answer.
Signup and view all the answers
If the discriminant is less than 0, you will have no real numbers.
Signup and view all the answers
If the discriminant equals 0, you will have 1 answer.
Signup and view all the answers
Study Notes
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
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Prepare for your Pre-Calculus (Algebra 2) test with these flashcards. This review covers essential formulas including the Distance, Midpoint, Quadratic, Circle, Slope, and Slope-Intercept formulas. Mastering these concepts will boost your confidence and performance on the test.
