Skip to main content
Back

Intermediate Algebra Key Concepts

Control buttons has been changed to "navigation" mode.
1/20

Terms in this set (20)

  • What is the general form of a linear function?
    A linear function is generally written as \(y=mx+b\), where m is the slope and b is the y-intercept.
  • How do you find the slope of a line from two points?
    The slope m is found by \(m=\frac{y_2 - y_1}{x_2 - x_1}\), the change in y over the change in x.
  • What does the y-intercept represent in a linear function?
    The y-intercept b is the point where the line crosses the y-axis, or where \(x=0\).
  • How do you graph a linear function given its equation?
    Plot the y-intercept, then use the slope to find another point by rising and running from the intercept, then draw the line through the points.
  • What is an exponent?
    An exponent indicates how many times a base number is multiplied by itself, written as \(a^n\).
  • What is the product rule for exponents?
    When multiplying like bases, add the exponents: \(a^m \times a^n = a^{m+n}\).
  • What is the quotient rule for exponents?
    When dividing like bases, subtract the exponents: \(\frac{a^m}{a^n} = a^{m-n}\), where a ≠ 0.
  • What is the zero exponent rule?
    Any nonzero base raised to the zero power equals 1: \(a^0 = 1\).
  • How do you find the greatest common factor (GCF) of two numbers?
    The GCF is the largest number that divides both numbers exactly, found by listing factors or using prime factorization.
  • What is factoring by graphing?
    Factoring by graphing involves finding the roots of a quadratic by graphing and then writing the expression as a product of linear factors.
  • How do you factor a quadratic using its roots?
    If the roots are \(r_1\) and \(r_2\), the quadratic factors as \((x - r_1)(x - r_2)\).
  • What is the difference between the greatest common factor and least common multiple?
    The GCF is the largest shared factor of numbers; the LCM is the smallest shared multiple.
  • How do you simplify expressions with exponents?
    Apply exponent rules such as product, quotient, and power rules to combine or reduce powers.
  • What is the power rule for exponents?
    When raising a power to another power, multiply the exponents: \((a^m)^n = a^{mn}\).
  • How do you graph a linear function from a table of values?
    Plot each (x, y) pair from the table on the coordinate plane and draw a line through the points.
  • What does the slope tell you about a line's graph?
    The slope indicates the steepness and direction; positive slopes rise, negative slopes fall.
  • How do you find the GCF using prime factorization?
    List prime factors of each number and multiply the common prime factors.
  • What is the role of the y-intercept in graphing linear functions?
    It provides a starting point on the y-axis to begin plotting the line.
  • How can factoring help solve quadratic equations?
    Factoring rewrites the quadratic as a product of binomials, allowing use of the zero product property to find solutions.
  • What is the zero product property?
    If \(ab=0\), then either \(a=0\) or \(b=0\).