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Math 103 Review Test #2 Overview

Nov 18, 2024

Math 103 Fall 2024 - Review Test #2

Covered Sections

  • 3.1
  • 3.2
  • 3.3
  • 3.5
  • 4.1
  • 4.3
  • 4.4

Quadratic Functions

Graph and Formula

  1. Use the graph of the quadratic function ( f ) to write its formula as ( f(x) = a(x-h)^2 + k ).

Solving Quadratic Equations

  1. Solve the following quadratic equations:
    • a) ( 3x^2 = 27 )
    • b) ( x^2 + 10x = 8 )
    • c) ( 4x^2 = 727 )
    • Solve ( 16x^2 + 9 = 24 )

Motion of a Thrown Object

  1. Formula for vertical motion: ( h(t) = -16t^2 + v_0t + h_0 ) where:

    • ( v_0 = 30 ) feet per second
    • ( h_0 = 80 ) feet

    Tasks:

    • a. Write a formula ( h(t) ) that models the height after ( t ) seconds.
    • b. Calculate height after 2 seconds.
    • c. Determine when the object reaches maximum height (algebraically).
    • d. Find the maximum height.

Algebraic Expressions and Polynomials

  1. Write expressions in standard form.

  2. Solve and write answers in standard form.

  3. Find the equation to shift the graph of ( f ) by specified amounts.

Polynomial Division

  1. Divide first polynomial by second, state quotient and remainder:
  • a)
    • b) Divide 6.
  1. Divide polynomials.

Remainder and Factor Theorems

  1. Use the remainder theorem to find the remainder when ( f(x) ) is divided by ( x-k ).

  2. Polynomial given: ( f(x) = 3x^3 - 11x^2 - 35x + 75 )

  3. Use the factor theorem to decide if ( x-k ) is a factor for ( f(x) ) for the given ( k ).

Solving Equations

  1. Solve:
  • a)
    • b)
    • c) Solve 8.

Analyzing Quadratic Functions

  1. Given ( f(x) = x^2 + 4x - 1 ):
  • a. Find the coordinates of the vertex.
    • b. Determine if the vertex is a max or min.
    • c. Find the equation of the axis of symmetry.
    • d. Sketch the graph.
    • e. Determine intervals where ( f ) is increasing.
    • f. Determine intervals where ( f ) is decreasing.

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