Exam 3: Polynomial and Rational Functions

Solve the problem. -A ball is tossed upward. Its height after $t$ seconds is given in the table. Find a quadratic function to model the data. Use the model to determine when the ball reaches its maximum height, as well as the value of the maximum height.

Use synthetic division to perform the division. - $\frac { 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 } { x - 2 }$

Match the equation to the correct graph. - $y = - \frac { 1 } { 2 } ( x + 4 ) ^ { 2 } - 5$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 8 x ^ { 3 } + 9 x ^ { 2 } - 8 x - 5 ; - 2$ and $- 1$

Identify the vertex of the parabola. - $y = x ^ { 2 } - 12 x + 37$

Determine which of the rational functions given below has the following feature(s). -The $x$ -intercept is 2

Find the zeros of the polynomial function and state the multiplicity of each. - $4 x ^ { 7 } + x ^ { 5 }$

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x² should be positive or negative. -The amount of sales tax paid as a function of the sales price.

Solve. -The data in the table show the number of burglaries reported in a small town for several years on record. Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Give all possible rational zeros for the following polynomial. - $P ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 4 x ^ { 2 } + 18$

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = 2 + \mathrm { i } ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 3 } + 12$

Answer the question -If y varies directly as x, and x is doubled, how is y changed?

Provide an appropriate response. -Find a quadratic function $f$ having $x$ -intercepts $- 9$ and $- 2$ and $y$ -intercept 6 .

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 4 ) ^ { 2 } + 4$

Graph the function. - $f(x)=\frac{8}{x^{2}}$

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $2 x ^ { 8 } + 8 x ^ { 6 } + 7 x ^ { 4 } + 3 x ^ { 2 } + 8 = 0$

Provide an appropriate response. -How many positive real zeros does this graph have?

Provide an appropriate response. -What is the domain of the graph?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 64$

Determine which of the rational functions given below has the following feature(s). -There is a "hole" in its graph at $x = 4$