Exam 3: Polynomial and Rational Functions

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 20 x + 16$

Determine whether the graph shown is the graph of a polynomial function. -

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } - 3 x - 5$

Determine the maximum possible number of turning points for the graph of the function. -Suppose that a polynomial function is used to model the data shown in the graph below. Determine the degree of the polynomial function of best fit and the sign of the leading coefficient.

Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 4 x + 3$

Use synthetic division and the Remainder Theorem to find the indicated function value. - $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } - 4 x ^ { 2 } + 3 x + 7 ; f ( 4 )$

Write an equation that expresses the relationship. Use k as the constant of variation. -While traveling at a constant speed in a car, the centrifugal acceleration passengers feel while the car is turning is inversely proportional to the radius of the turn. If the passengers feel an acceleration of 20 feet per second per second when the radius of the turn is 80 feet, find the acceleration the passengers feel when the radius of the turn is 320 feet.

Solve Problems Involving Joint Variation - $x$ varies jointly as $y$ and the cube of $z$ .

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. - $6 x ^ { 3 } - 40 x ^ { 2 } + 54 x - 20 = 0 ; 1$

Find the domain and range of the quadratic function whose graph is described. -The vertex is $( 1,6 )$ and the graph opens down.

Divide using long division. - $\left( - 16 x ^ { 3 } + 32 x ^ { 2 } - 3 x - 15 \right) \div ( - 4 x + 5 )$

Determine whether the graph shown is the graph of a polynomial function. -

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = 4 x ^ { 2 } + 2 x + 2$

Solve the problem. -A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance in feet of the ball from the ground after $t$ seconds is $\mathrm { s } = 96 \mathrm { t } - 16 \mathrm { t } ^ { 2 }$ . For what interval of time is ball more than 128 above the ground?

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 6$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x + 3 } { x ^ { 2 } + 2 x - 5 }$

Solve the problem. -A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 244 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = x ^ { 5 } + 9 x ^ { 6 }$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $3 x ^ { 4 } - 17 x ^ { 3 } + 61 x ^ { 2 } - 73 x + 26 = 0$

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - $\mathrm { n } = 4 ; 2 \mathrm { i } , 7$ , and $- 7$ are zeros; leading coefficient is 1