Questions and Answers
What are the x-intercepts?
Plug in 0 for y.
What are the y-intercepts?
Plug in 0 for x.
What is the formula to find the vertex?
-b/2a.
What is the equation for a parabola?
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What value represents the axis of symmetry of a parabola?
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How do you find the maximum of a function?
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How do you find the domain of a function?
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How do you determine the equation of asymptotes?
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What is the first step when solving logarithms for x?
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What is done in the second step of solving logarithms for x?
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What is the process to convert from a log to its equivalent form?
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What is the general formula for compound growth questions?
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What is the definition of range in terms of graphing?
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What is the definition of domain in terms of graphing?
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What does it mean when an equation just says log?
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What is the process for expanding log(xy)?
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What does it mean when there is a negative in logarithms?
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Study Notes
Parabolas
- Vertex is calculated using the formula -b/2a.
- X-intercepts are found by setting y=0; solve for x.
- Y-intercepts are found by setting x=0; solve for y.
- Axis of symmetry is the k value from the vertex notation (vertex = (h, k)).
- Standard equation for a parabola is y = a(x-h)² + k.
- To find the maximum point of a parabola, use a graphing calculator to locate the maximum value on the equation.
Understanding Fractional Equations
- For equations resembling fractions, the domain includes all possible x values.
- X-intercepts are found by setting the numerator to 0, while Y-intercepts are found by making x=0.
- Asymptotes occur when the denominator equals 0.
Logarithmic Functions
- If no base is indicated in a logarithm, it is log base 10 (log10).
- When expanding logarithms involving an exponent, the exponent is brought in front: for example, y³ = 3 log y.
- In condensing logarithmic expressions, negative values move to the denominator.
- Fractions in front of logarithmic functions imply manipulation with radicals: the numerator goes inside the radical, and the denominator goes outside.
Logarithmic Properties
- Expanding log(xy) results in log x + log y.
- The addition of logarithms corresponds to multiplication, while subtraction indicates division.
- Steps to solve a logarithm for x:
- First: isolate by adding or subtracting the extra value.
- Second: divide out the extra value.
- Third: convert to the exponential form and solve using a calculator.
Transitions Between Logarithmic Forms
- When converting values into logs:
- Place log first.
- The initial number becomes the new exponent.
- The previous answer becomes the base.
- The previous exponent converts to the new answer.
- For conversion from logarithmic form to exponential:
- The original exponent becomes the base of the number.
- The previous answer converts to the exponent.
- The base number becomes the new resulting number.
Compound Interest Formula
- The formula for compound interest is A = P(1 + r/n)^(nt).
- Variables in this formula represent:
- A: the amount of money accumulated after n years, including interest.
- P: the principal amount (initial investment).
- r: annual interest rate (decimal).
- n: number of times that interest is compounded per year.
- t: time the money is invested for, in years.
Domain and Range
- The domain represents the range of x values (from left to right).
- The range illustrates the vertical extent (up and down) and can be analyzed with a calculator.
Intercepts and Asymptotes
- Y-intercepts occur when x=0, and can be found using a calculator.
- X-intercepts occur when y=0, also found via calculator.
- The equation of vertical asymptotes is defined as y= the dotted line in the graph.
Miscellaneous
- The notation A = Pert indicates:
- A: final amount.
- P: initial principal.
- e: base of the natural logarithm.
- r: interest rate.
- t: time in years.
Studying That Suits You
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Description
Test your knowledge of advanced algebra concepts with these flashcards. Focus on key topics such as parabolas, vertex calculations, and intercepts. Perfect for reviewing before your final exam in Advanced Algebra.
