Questions and Answers
What do you use when solving equations and inequalities?
Use inverse operations
Which of the following represents the inequality sign for greater than?
Which of the following represents the inequality sign for less than?
What is the inequality sign for greater than or equal to?
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What is the inequality sign for less than or equal to?
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What do you do when multiplying or dividing by a negative in inequalities?
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What does one solution to an equation look like?
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What does a no solution equation look like?
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What does infinite solutions to equations look like?
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What is the first step to solve the equation 3(2x+3)=6x+18+2x?
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How do you solve the inequality -8x + 7 > 35?
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What is the decay factor in the equation y = p(l - r)^t?
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What is the name of a quadratic function?
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What is the maximum or minimum point of a quadratic?
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How do you find the vertex of a quadratic?
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What are the zeros or roots of a function?
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How do you find the zeros or roots of a function?
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What is the standard form of a quadratic?
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What is vertex form?
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What is factored form?
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What is the axis of symmetry?
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What are the solutions of two or more functions?
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How do you find the rate of change over a given interval?
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How do you transform a quadratic?
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What is the discriminant of a quadratic?
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Study Notes
Equations and Inequalities
- Use inverse operations to solve equations and inequalities.
- Inequality signs:
- Greater than: >
- Less than: <
- Greater than or equal to: ≥
- Less than or equal to: ≤
- When multiplying or dividing by a negative in inequalities, flip the inequality sign.
Solutions to Equations
- One solution example: (X = #)
- No solution example: (12 = 8)
- Infinite solutions example: (13 = 13)
Solving Equations
- To solve (3(2x+3)=6x+18+2x), distribute, combine like terms, and isolate (x) to find (x = -4.5).
- To solve (-8x+7>35), subtract, divide, and remember to flip the inequality when dividing by a negative.
Quadratic Functions
- The decay factor in the formula (y = p(l - r)^t) must be between 0 and 1.
- A quadratic function is represented as a parabola.
- The vertex indicates the maximum or minimum point of a quadratic function.
Finding the Vertex
- Compute vertex using (x = -\frac{b}{2a}); substitute (x) back into the equation for (y).
Zeros and Roots of Functions
- The zeros or roots are the x-intercepts, where the function crosses the x-axis.
- Methods to find zeros/roots:
- Square Root Method
- Factoring
- Quadratic formula
- Completing the square
Forms of Quadratic Functions
- Standard form: (y = ax^2 + bx + c).
- Vertex form: (y = a(x - h)^2 + k).
- Factored form: (y = (x - p)(x - q)).
- Axis of symmetry is found at (x = -\frac{b}{2a}).
Intersections of Functions
- Solutions of two or more functions are found where they intersect.
Rate of Change
- To find the rate of change over a given interval, identify the two points on the graph and calculate the slope ((rise/run)).
Transforming Quadratics
- Transformation equation: (y = a(x \pm h)^2 \pm k).
- (+h): move left
- (-h): move right
- (+a): opens upward
- (-a): opens downward
Discriminant of a Quadratic
- Calculated by (b^2 - 4ac):
- Positive: two solutions
- Negative: no real solutions
- Zero: one solution
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Description
This quiz covers key concepts related to solving equations and inequalities using inverse operations. It includes topics such as inequality signs, examples of solutions, and methods for solving linear and quadratic functions. Test your understanding of these fundamental algebraic principles.