10.3 vertex and max values with comparing functions 2016 ink.notebook. March 14, Vertex and Max Value & Page 101.

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1 10.3 vertex and max values with comparing functions 2016 ink.notebook Page 101 Page Vertex and Value and Comparing Functions Algebra: Transformations of Functions Page 103 Page 104 Lesson Objectives Standards Lesson Notes 10.3 Vertex and Value & Comparing Functions 1

2 Algebra: Transformations of Functions Lesson Objectives Standards Lesson Notes A.SSE.3 I will find the maximum or minimum value from a quadratic equation F.IF.9 I will compare linear, quadratic, or exponential functions (graphed vs table vs algebraic vs verbal) F.LE.1 I will distinguish between linear, quadratic, or exponential functions (know doubling is exp) F.LE.3 I will distinguish between linear, quadratic, or exponential functions Algebra: Transformations of Functions Lesson Objectives Standards Lesson Notes A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. b) Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a) Graph linear and quadratic functions and show intercepts, maxima, and minima. y = mx + b - Linear y = ax 2 + bx + c - Quadratic remember: (1 + r) = growth (1 - r) = decay y = a x - h + k - Square Root y = a(b) x 2

3 10.3 vertex and max values with comparing functions 2016 ink.notebook Tell if each equation is linear, quadratic, or exponential. 1. y = 2 x 2. y = 2x y = x 2 Tell whether each equation is an exponential growth or decay. 7. y = 2500( )x 8. y = 1000(1.11)x Tell if each graph is linear, quadratic, or exponential y = 500(1 +.05)x The parabola is symmetric with respect to the dashed vertical line that contains the vertex. This line is called the axis of symmetry. The equation of the axis of symmetry: x= -b 2a This value is also the x coordinate of the vertex. 3

4 axis y of sym or x-int x-int x y-int vertex Equation of the axis of symmetry x = -b 2a Vertex (also used to find the max or min value) (-b -b 2a, f(x)( 2a ) Plug your answer back into the equation to find the y value. EXAMPLE: y = 3x 2 + 6x + 2 Equation of the axis of symmetry x = -6 2(3) x = - 1 Vertex y = 3( - 1) 2 + 6( - 1) + 2 y = 3(1) y = - 1 ( - 1, - 1) 4

5 10.3 vertex and max values with comparing functions 2016 ink.notebook Find the axis of symmetry and the vertex for each function. 10. y = x2 + 2x y = x2 + 2 Find the axis of symmetry and the vertex for each function. 12. y = 2x2 8x y = 5x2 + 4x 8 5

6 10.3 vertex and max values with comparing functions 2016 ink.notebook 14. Mrs. Truro sells packages of towels. She uses the formula, p = x2 + 50x 350, where p is her profit from selling x packages of towels, to approximate her profits per day. a) How many packages of towels must she sell to make a maximum profit? b) What is the maximum profit? 15. The formula for the cost of running a taco stand is c = x2 12x a) How many units of x tacos must be sold to keeps costs at a minimum? b) What is the minimum cost? 6

7 On Your Whiteboards Find the axis of symmetry and the vertex for the function. a) y = x 2 + 6x 5 b) fraction! y = x 2 5x + 4 c) The owner of a new company finds that the profit p is related to the number of x items sold by p = x x a) How many items must be sold for the maximum profit? b) What is the maximum profit? On the Worksheet 7

8 Homework Homework Homework Hint State whether each has a max or min. REMINDER: If it opens ( ), then it has a min. If it opens ( ), then it has a max. 1. y = x 2 2. y = 4x 2 or min or or or max or 3. y = x 2 4. y = 4x 2 or max or or min or Find the axis of symmetry and the vertex for each function. 5. y = x 2 6x 8 6. y = x 2 4x + 3 Find the axis of symmetry and the vertex for each function. 7. y = x 2 8x y = 4x x 6 8

9 Find the axis of symmetry and the vertex for each function. 9. y = x 2 6x y = 2x The formula for the height h reached by a rocket fired straight for the ground with an initial velocity of 96 ft/s is modeled by h = 16t t. a) Find the time t for the rocket to reach a maximum height. b) What is the maximum height? 12. The formula for the cost of producing x units of radios is c = x 2 12x a) How many radios should be made to produce the minimum cost? Tell if each equation is linear, quadratic, or exponential. 13. y = 3(x+ 1) linear quadratic exponential linear quadratic exponential b) What is the minimum cost? 15. linear quadratic exponential 16. y = 5 x + 1 linear quadratic exponential 9

10 Tell if each graph is linear, quadratic, or exponential Tell whether each equation is an exponential growth or decay. 23. y = 750( ) x Tell whether each graph is an exponential growth or decay y = 10500(1 +.12) x 25. y = 250(1.034) x 10

11 ANSWERS: 1), min 3), max 5) x = 3, ( 3, 1) 7) x = 4, (4, 9) 9) x = 3, (3, 2) 11) a) 3 seconds b) 144 feet 13) quad 15) linear 17) linear 19) exponential 21) quadratic 23) decay 25) decay 27) growth 11