Advanced Algebra Final Exam Flashcards

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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?

<p>y = a(x-h)^2 + k.</p> Signup and view all the answers

What value represents the axis of symmetry of a parabola?

<p>The k value of the vertex.</p> Signup and view all the answers

How do you find the maximum of a function?

<p>Put in the equation to the calculator and click the maximum button.</p> Signup and view all the answers

How do you find the domain of a function?

<p>All the values x can be.</p> Signup and view all the answers

How do you determine the equation of asymptotes?

<p>Set the denominator to zero.</p> Signup and view all the answers

What is the first step when solving logarithms for x?

<p>Subtract or add the extra value.</p> Signup and view all the answers

What is done in the second step of solving logarithms for x?

<p>Divide off the extra value.</p> Signup and view all the answers

What is the process to convert from a log to its equivalent form?

<p>The old exponent becomes the big number, the old answer becomes the new exponent, and the big number becomes the new answer.</p> Signup and view all the answers

What is the general formula for compound growth questions?

<p>A = P(1 + percent/number of times a year)^(number of times a year)(amount of years).</p> Signup and view all the answers

What is the definition of range in terms of graphing?

<p>Up and down, use calculator.</p> Signup and view all the answers

What is the definition of domain in terms of graphing?

<p>X-range left to right.</p> Signup and view all the answers

What does it mean when an equation just says log?

<p>That means log10.</p> Signup and view all the answers

What is the process for expanding log(xy)?

<p>It would be logx + logy.</p> Signup and view all the answers

What does it mean when there is a negative in logarithms?

<p>The value goes in the denominator of the fraction.</p> Signup and view all the answers

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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.

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