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Ch 5 Pt 1 (5-1 5-3) Portfolio Page -- Algebra 2 Lesson 5-1: Modeling Data with Quadratic Functions --identify quadratic functions & their graph --Quadratic regression on graphing calculator STANDARD FORM OF QUADRATIC FUNCTION: y = ax2 + bx + c Quadratic term: ax2 Linear term: bx Constant term: c Example: Determine if the function is linear or quadratic. State the quadratic, linear, and constant terms: GRAPH OF A QUADRATIC FUNCTION: Parabola – the graph of a quadratic function (U-shaped) Axis of Symmetry -- the line that divides a parabola into two parts that are mirror images. Vertex – the point at which the parabola intersects the axis of symmetry. If graph opens up, vertex is MINIMUM. If graph opens down, vertex is MAXIMUM. P Q Example: 1) State 2) State 3) State 4) State vertex: axis of symmetry: P’ Q’ QUADRATIC REGRESSION ON GRAPHING CALCULATOR: Write a quadratic model given points on the graph. In calculator: Find the quadratic model for the values (1, 0), (2 , -3), (3, -10) 1) Turn Plots on/Turn Diagonistics ON (Catalog) 2) STAT / 1:Edit – enter x values in L1 and y values in L2 3) STAT / CALC / 5:QuadReg/ /Enter L , L 1 2 4) Y=/VARS/5:Statistics/EQ/1:RegEQ The quadratic function is _____________________________ Example: The number of weekend get-away packages a hotel can sell can be modeled by R = -0.12p2+ 60p, where p is the price of a get-away package and R is the hotel’s revenue. What price will maximize the revenue? What is the maximum revenue? Predict the hotel’s revenue if the cost of a get-away package is $100. Lesson 5-2: Properties of Parabolas --graphing from standard form --finding minimum and maximum values of quadratic functions GRAPH FROM STANDARD FORM: f(x) = ax2 + bx + c: 1) 2) If a is (+), parabola opens up. If a is (-), parabola opens down. 3) Vertex: ( 4) 5) −𝒃 −𝒃 , 𝒇( )) 𝟐𝒂 𝟐𝒂 Axis of symmetry: x = Y-intercept: (0, c) −𝒃 𝟐𝒂 ALL GRAPHS SHOULD INCLUDE: --axis of symmetry --vertex --two pts to left and right of vertex Graph: (y = ax2 + c) Graph: (y = ax2 + bx + c) Lesson 5-3: Translating Parabolas --Using Vertex Form to graph and write equations VERTEX FORM OF QUADRATIC FUNCTION: y = a(x – h)2 + k Vertex: (h, k) Axis of Symmetry: x = h Graph: WRITING EQUATIONS: Given vertex and one point Example: IDENTIFY VERTEX AND Y-INTERCEPT FOR EACH FUNCTION: Example (standard form) Example (vertex form) STANDARD FORM/VERTEX FORM: Convert the function to standard form: Convert the function to vertex form: