Math Exam 2: Further help
Math Exam 2: Further help MATH 1101
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This 3 page Study Guide was uploaded by Alexandra Reshetova on Sunday February 21, 2016. The Study Guide belongs to MATH 1101 at Georgia State University taught by Haiqi Wang in Winter 2016. Since its upload, it has received 71 views. For similar materials see Introduction to Mathematical Modeling in Mathematics (M) at Georgia State University.
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Date Created: 02/21/16
Math Exam 2 Study Guide (further help) Quadratic Functions Examples of Polynomial Functions: 1. f(x) = x^2 – x + 17 2. f(x) = -8 3. f(x) = x^3 + 4x Examples of Non-Polynomial Functions: 1. f(x) = 3x-7 2x+8 2. f(x) = Square root of x + 4 3. f(x) = Absolute value of 4x+5 Quadratic Function formulas: 1. f(x) = ax^2 + bx + c (a does not = 0) 2. f(x) = a (x-h)^2 + k Quadratic equation can be solved in four ways: 1. Applying square root property 2. By Factoring 3. Applying the formulas 4. Completing the square Solve by using square root property: 1. If x^2 = c, then x = square root c or x = negative square root c Example: x^2 = 48 x = Plus or minus square root 48 x = Plus or minus 4 square root 3 Solving by Factoring: 1. Put all terms to one side of equation 2. Factor 3. Apply zero Product Property Solving by applying the formulas: 1. Simply plug into equation 2. Solve Solve by completing the square: 1. Multiply b by ½ 2. Square the result Example: x^2 + 8x 8(1/2) = 4 (4)^2 = 16 x^2 + 8x + 16 = (x+4)^2 Completing the Square definition : finding the value that makes a quadratic function become a square trinomial Another example: x^2 – 10x = -16 (-10)(1/2)= -5 (-5)^2 = 25 x^2 -10x + 25 = -16 +25 (x-5)^2 = 9 x-5 = plus or minus square root 9 x-5 = plus or minus 3 x = 5 plus or minus 3 x = 8 or x = 2 Quadratic Formula: X = -b plus or minus square root b^2 – 4ac 2a The Parabola: (basic is y = x^2) Equations: 1. y = ax^2 + bx +c 2. y = a(x-h)^2 + h Vertexes: 1. (-b/2a , c- (b^2 / 4a)) 2. (k,h) Axis of Symmetry: 1. x = -b / 2a 2. x = k Direction: 1. up if a is greater than zero 2. down if a is less than zero Max and Min values: 1. Opens Up: Minimum (at h) (no max) 2. Opens Down : Maximum (at h) (no min) Vertical Shift: (y = x^2 + h) 1. h positive = up 2. h negative = down Horizontal Shift: (y = (x-k)^2 ) 1. k positive = right 2. k negative = left Vertical Stretch: 1. y = ax^2 is a vertical stretch by factor of a Reflection over x-axis: 1. y = -x^2 is a mirror image of y = x^2
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