MAT-121 Written Assignment 4.docx - MAT-121 COLLEGE ALGEBRA...

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MAT-121: COLLEGE ALGEBRA Written Assignment 4 2.5 points each SECTION 5.1 Algebraic For the following exercise, rewrite the quadratic function in standard form and give the vertex. 1. y = 4 x 2 + 5 x 7 h = 5 2 ( 4 ) h = 5 8 k = 4 ( 5 8 ) 2 + 5 ( 5 8 ) 7 k = 4 ( 25 64 ) + 5 ( 5 8 ) 7 k = 25 16 25 8 7 k = 25 16 50 16 112 16 k = 137 16 Vertex: ( 5 8 , 137 16 For the following exercise, determine whether there is a minimum or maximum value to the quadratic function. Find the value and the axis of symmetry. 2. y = 1 3 x 2 4 x + 9 h = 4 2 3 h = 6 Minimum is -3 which occurs at 6. k = 1 3 ( 6 ) 2 4 ( 6 ) + 9 k = 12 24 + 9 k =− 3 Axis of symmetry: x = 6 ) Copyright © 2019 by Thomas Edison State University. All rights reserved.
For the following exercise, rewrite the quadratic function in standard form and give the vertex. Determine whether there is a minimum or maximum value to the quadratic function. Find the value and the axis of symmetry. Determine the domain and range of the quadratic function.
For the following exercise, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.
5. An athletic stadium holds 105,000 fans. With a ticket price of $22, the average attendance has been 32,000. When the price dropped to $16, the average attendance rose to 50,000. Assuming that attendance is linearly related to ticket price, what ticket price would maximize revenue? Round ticket price to the nearest ten cents.
Copyright © 2019 by Thomas Edison State University. All rights reserved.
h = 98000 2 (− 3000 ) h = $ 16.33 Copyright © 2019 by Thomas Edison State University. All rights reserved.
SECTION 5.2 Algebraic For the following exercise, identify the function as a power function, a polynomial function, or neither. 6. f ( x )= 4 ( x 3 ) 3 Power function For the following exercise, find the degree and leading coefficient for the given function if it is a polynomial. If it is not a polynomial, then state so. 7. f ( x )= ( 2 x 2 5 ) 2 + ( x 3 ) 2 + 5 f ( x ) = ( 2 x 2 5 ) ( 2 x 2 5 ) + ( x 3 ) ( x 3 ) + 5 f ( x ) = 4 x 4 19 x 2 6 x + 39 Leading coefficient & leading degree are both 4. For the following exercise, find the intercepts of the functions. 8. g ( x )= ( 3 x 2 10 x 8 ) ( x + 3 ) g ( 0 ) = ( 3 ( 0 ) 2 10 ( 0 ) 8 ) ( 0 + 3 ) g ( 0 ) =− 24 y intercept is ( 0 , 24 ) 0 = ( 3 x 2 10 x 8 ) ( x + 3 ) 0 = ( x 4 ) ( 3 x + 2 ) ( x + 3 ) 0 = x 4 x intercepts are ( 4,0 ) x = 4 0 = 3 x + 2 x = 2 3 0 = x + 3 x =− 3 ( 2 3 , 0 ) , ( 3,0 ) Technology For the following exercise, graph the polynomial function using a calculator or a graphing utility. Based on the graph, determine the intercepts and the end behavior. 9. f ( x )= x 6 36 x intercepts : ( 1.81,0 ) ( 1.81,0 ) y intercept : ( 0 , 36 ) x→ ∞, f ( x ) →∞ ¿ x→∞ ,f ( x ) →∞ Copyright © 2019 by Thomas Edison State University. All rights reserved.
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