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=4×2+5x-7

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.

0. y=13×2-4x+9

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.

0. f(x)=-12×2+4x-2

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.

0. (h, k) = (-1, 3),

(x, y) = (-2, 6)

Real-World Applications

0. 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.

SECTION 5.2

Algebraic

For the following exercise, identify the function as a power function, a polynomial function, or neither.

0. f(x)=4×33

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.

0. f(x)=2×2-52+x-32+5

For the following exercise, find the intercepts of the functions.

0. g(x)=3×2-10x-8x+3

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.

0. f(x)=x6-36

Real-World Applications

For the following exercise, use the written statement to construct a polynomial function that represents the required information.

0. A cube has an edge of 2.25 feet. The edge is increasing at the rate of 1.25 feet per hour. Express the volume of the cube as a function of h, the number of hours elapsed.

SECTION 5.3

Algebraic

For the following exercise, find the x-intercept of the polynomial function. Express the intercept in point (ordered pair) form.

0. f(x)=5×3-20×2+2x-8

For the following exercise, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval.

0. g(x)= -3×3-12×2+11x between x = -5 and x = -4

Graphical

For the following exercise, graph the polynomial function. Note x- and y-intercepts, multiplicity, and end behavior.

0. f(x)=x(x+4)(x-4)(x+7)

For the following exercises, use the given information about the polynomial graph to write the equation.

0. Degree 3; zeros at x=-1,x=4,x=-5; passes through the point (2, -84)

Real-World Applications

0. A cylinder has a radius of 2x+3units and a height of 5