Factor the polynomial function \( f ( x ) \) . Then solve the equation \( f ( x ) = 0 \) . 

\( f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 9 x - 18\) 

The factored polynomial function is \( f ( x ) = \square \) . (Factor completely.) 

The solutions of the equation \( f ( x ) = 0 \) are \( \square \) . 

(Use a comma to separate answers as needed.) 

A town currently has \( 4000 \) residents. The expected future population can be approximated by the function \( p ( x ) = 4000 ( 1.117 ) ^ { 0.1 x } \) where \( x \) is the number of years in the future. Determine the expected population of the town in \( 10 \) years, and in \( 50 \) years. 

A) \( 5,225 \) and \( 7,358 \) 

B) \( 40,445.04 \) and \( 202,225.22 \) 

C) \( 4,468 \) and \( 1.78 \times 1018 \) 

D) \( 4,468 \) and \( 6,955\) 

 A ball is shot from a cannon into the air with an upward velocity of \( 40 ft / sec \) . The equation that gives the height (h) of the ball at any time ( \( t ) \) is: \( h ( t ) = - 16 t ^ 2 + 40 ft + 1.5 \) . Find the maximum height attained by the ball. 

Find an equation of the line having the given slope and containing the given point. Then graph the line passing through the given point and having the given slope on the provided graph worksheet or graph paper. 

\( m = 0 , ( 0 , - 6 ) \) 

The equation of the line is \( y = \square \) Use the provided graph worksheet or graph paper to graph the line and upload a picture of your graph in the following question. Use the given point and slope when drawing the line. 

For the graph shown below do the following. 

a. Find the zeros and state the multiplicity of each zero. 

b. Write an equation, expressed as the product of factors, of a polynomial function for the graph. Use a leading coefficient of \( 1 \) or - \( 1 \) and make the degree of \( f \) as small as possible. 

c. Use both the equation in part (b) and the graph to find the \( y \) -intercept 

a. List the zeros whose multiplicity is even. Select the correct choice below and fill in any answer boxes within your choice. 

A. \(\square \)(Use a comma to separate answers as needed.) 

B. There are no such zeros. 

List the zeros whose multiplicity is odd. Select the correct choice below and fill in any answer boxes within your choice. 

A. \(\square \)(Use a comma to separate answers as needed.) 

B. There are no such zeros. 

b. Write an equation, expressed as the product of factors, of a polynomial function for the graph. Use a leading coefficient of \( 1 \) or \( - 1 \) and make the degree of \( f \) as small as possible. 

\( f ( x ) = \square \) 

(Type your answer in factored form.) 

c. The y-intercept is \(\square \)