math flashcard

Factoring a Quadratic Expression

To factor a quadratic expression of the form ax² + bx + c, follow these steps: first, factor out the greatest common factor (if applicable). Next, identify two numbers that multiply to c (when a = 1) or c/a (when a ≠ 1) and add to b. Finally, express the quadratic as a product, using the form a(x + j)(x + k) where j and k are the numbers found.

Probability

Probability is a measure of the likelihood of an event occurring. For mutually exclusive events A and B, the probability of either event occurring is found by adding their individual probabilities.

Probability of A and B occurring

The combined probability of two independent events A and B occurring simultaneously is calculated by multiplying their individual probabilities: P(A and B) = P(A) * P(B). This assumes that the occurrence of one event does not affect the other.

Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in geometry, specifically applying to right triangles. It states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), expressed as a² + b² = c².

Slope Formula

The Slope Formula is used to determine the steepness or inclination of a line on a graph. It is calculated using the difference in the y-coordinates (y2 - y1) divided by the difference in the x-coordinates (x2 - x1), giving the formula m = (y2 - y1) / (x2 - x1).

Distance Formula

The Distance Formula calculates the straight-line distance between two points (x1, y1) and (x2, y2) in a Cartesian plane. It is derived from the Pythagorean Theorem and is expressed as d = √((x2 - x1)² + (y2 - y1)²).

Quadratic Formula

The Quadratic Formula is a key equation used for solving quadratic equations of the form ax² + bx + c = 0. It provides the values of x that satisfy the equation and is given by x = (-b ± √(b² - 4ac)) / (2a), where 'b² - 4ac' is known as the discriminant.