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Questions and Answers
What is the formula for exponential growth?
What is the formula for exponential growth?
What is the formula for exponential decay?
What is the formula for exponential decay?
What does the Quadratic Formula calculate?
What does the Quadratic Formula calculate?
x = -b ± √(b² - 4ac)/2a
Match the discriminant rules with their outcomes:
Match the discriminant rules with their outcomes:
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What is the discriminant formula?
What is the discriminant formula?
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What does 'b' represent in the context of a function?
What does 'b' represent in the context of a function?
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Complete the sentence: For m: as x ___ 1, y ___ m.
Complete the sentence: For m: as x ___ 1, y ___ m.
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What is the term for the x-intercept?
What is the term for the x-intercept?
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What does 'Minimum' refer to in a function?
What does 'Minimum' refer to in a function?
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What does 'Maximum' refer to in a function?
What does 'Maximum' refer to in a function?
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What is the characteristic of Linear Growth?
What is the characteristic of Linear Growth?
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What characterizes exponential growth?
What characterizes exponential growth?
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Study Notes
Exponential Growth and Decay
- Exponential Growth Formula: y = a(1 + r)^t, where 'a' is the starting value, 'r' is the growth rate, and 't' is time.
- Exponential Decay Formula: y = a(1 - r)^t, affecting the same variables as growth but indicating a decrease.
Quadratic Functions
- Quadratic Formula: x = -b ± √(b² - 4ac)/2a, used to find the roots of quadratic equations.
- Discriminant Formula: d = b² - 4ac, determines the nature of the roots based on its value.
Discriminant Rules
- Two Solutions: Occurs when d > 0, meaning there are two distinct real solutions.
- No Solutions: When d < 0, indicating that there are no real solutions.
- One Solution: Happens when d = 0, resulting in exactly one real solution.
Characteristics of Functions
- 'b' as Starting Value: In the context of exponential functions, 'b' indicates the initial value of 'y'.
- Rate of Change: For a constant m, as 'x' increases by 1, 'y' increases by m, representing a linear growth scenario.
Features of Graphs
- Zero (x-intercept): The point where the graph intersects the x-axis, indicating where y equals zero.
- Minimum Value: Refers to the lowest y-value achieved on the graph, indicating the lowest point of the function.
- Maximum Value: Denotes the highest y-value on the graph, representing the peak of the function.
Growth Models
- Linear Growth: Characterized by a consistent increase of the same amount over intervals.
- Exponential Growth: Features a changing increase, where the addition grows disproportionately over time, highlighted by the growth formula.
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Description
Prepare for your SAT with these Algebra 2 flashcards. Each card explains essential concepts such as exponential growth, quadratic formulas, and discriminant rules, providing you with a quick reference for critical algebraic formulas. Boost your confidence and mastery in Algebra 2 as you get ready for the exam!
