Podcast
Questions and Answers
What is the Slope-Intercept Form?
What is the Slope-Intercept Form?
- y = mx + b (correct)
- y - y₁ = m(x - x₁)
- Ax + By = C
- h = -16t² + vt + s
What is the Point-Slope Form?
What is the Point-Slope Form?
y - y₁ = m(x - x₁)
What is the Standard Form of a linear equation?
What is the Standard Form of a linear equation?
Ax + By = C
What is the formula for the Quadratic Formula?
What is the formula for the Quadratic Formula?
What is the Distance Formula?
What is the Distance Formula?
What is the Midpoint Formula?
What is the Midpoint Formula?
What is the Vertical Motion Model formula?
What is the Vertical Motion Model formula?
What does the Pythagorean Theorem state?
What does the Pythagorean Theorem state?
What is the X-Coordinate of the Vertex of a Quadratic?
What is the X-Coordinate of the Vertex of a Quadratic?
Flashcards
Slope-Intercept Form
Slope-Intercept Form
y = mx + b, where m is the slope and b is the y-intercept
Point-Slope Form
Point-Slope Form
y - y₁ = m(x - x₁), uses a point (x₁, y₁) and slope (m).
Standard Form
Standard Form
Ax + By = C, where A, B, and C are constants.
Distance Formula
Distance Formula
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Midpoint Formula
Midpoint Formula
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Vertical Motion Model
Vertical Motion Model
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Pythagorean Theorem
Pythagorean Theorem
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Study Notes
Slope and Line Equations
- Slope Formula: Used to determine the steepness of a line; denoted as m = (y₂ - y₁) / (x₂ - x₁).
- Slope-Intercept Form: Represents linear equations in the form y = mx + b, where m is the slope and b is the y-intercept.
- Point-Slope Form: A specific form for linear equations, expressed as y - y₁ = m(x - x₁), utilizes a known point (x₁, y₁) on the line.
Standard and Quadratic Forms
- Standard Form: Represents linear equations in the format Ax + By = C, where A, B, and C are constants, often used for graphing.
- Quadratic Formula: Used to find the roots of quadratic equations, given by x = (-b ± √(b² - 4ac)) / (2a).
Distance and Midpoint
- Distance Formula: Calculates the distance between two points (x₁, y₁) and (x₂, y₂) as d = √((x₂ - x₁)² + (y₂ - y₁)²).
- Midpoint Formula: Determines the exact midpoint between two points, calculated as M = ((x₁ + x₂)/2, (y₁ + y₂)/2).
Physics in Motion
- Vertical Motion Model: Models the height of an object in free fall as h = -16t² + vt + s, where h is height, t is time, v is initial velocity, and s is initial height.
Geometry and Theorems
- Pythagorean Theorem: Fundamental relation in Euclidean geometry for right triangles, expressed as a² + b² = c², relating the lengths of the sides.
- X-Coordinate of Vertex of Quadratic: Determined using the formula x = -b/(2a), useful for finding the maximum or minimum point of a parabolic graph.
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