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Questions and Answers
What is the general form of a linear equation?
What is the general form of a linear equation?
- ax + by = c (correct)
- ax^2 + bx + c = 0
- x + by = c
- x^2 + bx + c = 0
What is the formula to solve quadratic equations when factoring is not possible?
What is the formula to solve quadratic equations when factoring is not possible?
- x = (b ± √(b^2 - 4ac)) / a
- x = (-b ± √(b^2 - 4ac)) / 2a (correct)
- x = (b ± √(b^2 + 4ac)) / 2a
- x = (-b ± √(b^2 + 4ac)) / 2a
What is the method to solve a system of equations where you solve one equation for one variable and substitute it into another equation?
What is the method to solve a system of equations where you solve one equation for one variable and substitute it into another equation?
- Elimination
- Substitution (correct)
- Graphing
- Factoring
What is the key feature of a quadratic equation graph that is the point where the axis of symmetry intersects the graph?
What is the key feature of a quadratic equation graph that is the point where the axis of symmetry intersects the graph?
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What is the definition of a quadratic equation?
What is the definition of a quadratic equation?
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What is the method to express a quadratic equation as a product of two binomials?
What is the method to express a quadratic equation as a product of two binomials?
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Study Notes
Algebraic Equations
- Linear Equations:
- Definition: An equation in which the highest power of the variable (usually x) is 1.
- General form: ax + by = c, where a, b, and c are constants.
- Example: 2x + 3 = 7
- Quadratic Equations (covered in more detail below)
- Systems of Equations:
- Definition: A set of two or more equations with two or more variables.
- Methods to solve:
- Substitution
- Elimination
- Example: 2x + 3y = 7, x - 2y = -3
Quadratic Equations
- Definition: An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠0.
- Factoring:
- Definition: Expressing a quadratic equation as a product of two binomials.
- Example: x^2 + 5x + 6 = (x + 3)(x + 2) = 0
- Quadratic Formula:
- Definition: A formula to solve quadratic equations when factoring is not possible.
- Formula: x = (-b ± √(b^2 - 4ac)) / 2a
- Example: Solve x^2 + 4x + 4 = 0
- Graphing Quadratic Equations:
- Definition: A visual representation of a quadratic equation on a coordinate plane.
- Key features:
- Vertex (h, k)
- Axis of symmetry
- x-intercepts
Algebraic Equations
- Linear Equations:
- Defined as equations with the highest power of the variable (usually x) being 1
- General form: ax + by = c, where a, b, and c are constants
- Example: 2x + 3 = 7
Quadratic Equations
- Definition: Equations of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠0
- Factoring:
- Expressing a quadratic equation as a product of two binomials
- Example: x^2 + 5x + 6 = (x + 3)(x + 2) = 0
- Quadratic Formula:
- Formula to solve quadratic equations when factoring is not possible
- Formula: x = (-b ± √(b^2 - 4ac)) / 2a
- Example: Solve x^2 + 4x + 4 = 0
- Graphing Quadratic Equations:
- Visual representation of a quadratic equation on a coordinate plane
- Key features:
- Vertex (h, k)
- Axis of symmetry
- x-intercepts
Systems of Equations
- Definition: A set of two or more equations with two or more variables
- Methods to solve:
- Substitution
- Elimination
- Example: 2x + 3y = 7, x - 2y = -3
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