Chapter 4: Linear and Quadratic Functions
Chapter 4: Linear and Quadratic Functions MAT 109
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This 4 page Bundle was uploaded by Sterling on Wednesday September 14, 2016. The Bundle belongs to MAT 109 at Barry University taught by Dr. Singh in Fall 2016. Since its upload, it has received 31 views. For similar materials see Precalculus Mathematics 1 in Mathmatics at Barry University.
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Date Created: 09/14/16
MAT 109 PreCalculus Mathematics 1 4.1 Linear Functions and Their Properties Notes L. Sterling August 29th, 2016 Abstract Give a de▯nition to each of the terms listed in this section. 1 Linear Function Any function in the form of f(x) = mx + b. 2 Nonlinear Function Any function that are not linear. 3 Linear Function’s Average Rate of Change ▯y f(x2) ▯ f1x ) m = = ▯x x2▯ x1 4 Increasing, Decreasing, and Constant Linear Functions 4.1 Increasing When a linear function is increasing over its given domain, its slope will be positive. 4.2 Decreasing When a linear function is decreasing over its given domain, its slope will be negative. 4.3 Constant When a linear function is constant over its given domain, its slope will be zero. 1 5 Quantity Supplied The price of any product that a company’s actually willing to make available for sale. 6 Quantity Demanded The price of any product that the consumers are actually willing to to pay. 7 Equilibrium Price The price at when the supplied quantity is equaled to the demanded quantity, which by equation is S(p) = D(p). 8 Equilibrium Quantity The demanded or supplied amount at the equilibrium price. 2 MAT 109 PreCalculus Mathematics 1 4.3 Quadratic Functions and Their Properties Notes L. Sterling August 29th, 2016 Abstract Give a de▯nition to each of the terms listed in this section. 1 Quadratic Function 2 Any second-degree function (parabola) in the form of f(x) = ax + bx + c with both a 6= 0 and a, b, and c are real numbers and that has a domain of all real numbers. 2 Newton’s Second Law of Motion Force equals mass times acceleration, which can be written as the following: F = ma 3 Opens Up When a parabola look like a \U" and have a lowest point called to absolute minimum. 4 Opens Down When a parabola look like a re ected \U" and have a highest point called to absolute maximum. 5 Method 2 f(x) = ax + bx + c 2 b f(x) = a(x ax) + c 1 b 2 b 2 b2 h = ▯ 2a h = (▯ 2a) = 4a2 2 2 2 b b b f(x) = a(x + x + 2) + c ▯ a( 2) a 4a 4a b b2 f(x) = a(x + x) + c ▯ a( ) a 4a 2 2 b 2 b f(x) = a(x + ax) + c ▯ 4a b2 4ac ▯ b2 k = c ▯ = 4a 4a 2 2 b 2 4ac ▯ b f(x) = a(x + ax) + 4a h = ▯ b 4ac▯b2 2a 4a 2 2 f(x) = ax + bx + c = a(x ▯ h) + k V ertex : (h;k) 6 Properties of a Quadratic Function’s Graph f(x) = ax + bx + c a 6= 0 V ertex : (▯b ;f(▯ b )) 2a 2a b Axis Symmetry : x = ▯ 2a Opens Up : a > 0 ! V ertex : Min point Opens Down : a < 0 ! V ertex : Max point 7 Quadratic Function’s X-Intercepts 7.1 Less Than 0 f(x) = ax + bx + c would have only two distinct x-intercepts if the following happens: b ▯ 4ac < 0 7.2 Greater Than 0 f(x) = ax + bx + c would have only no distinct x-intercepts if the following happens: 2 b ▯ 4ac > 0 7.3 Equal To 0 2 f(x) = ax + bx + c would have only one distinct x-intercept (at its vertex) if the following happens: 2 b ▯ 4ac = 0 2
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