13 Find the equation for a cubic polynomial that could gener

13) Find the equation for a cubic polynomial that could generate this graph given that it passes through the point (0,24)

y =

19) Using laws of exponents, rewrite the following expression as a quotient

e^(t-4) (t+9)

= __________

Sections 1.1-1.6: Problem 13 Previous Problem List Next 1 point) -2 1 that the vericel and horzontal scales are not the same) Note that the vertical and horizontal scales are not the same.) Find the equation for a cubic polynomial that could generate this graph given that it passes through the point (0,24) Sections 1.1-1.6: Problem 19 Previous Problem ListNext (1 point) Using laws of exponents, rewrite the following expression as a quotient. help (numbers) et-4(t +9) =

Solution

1) passes through (0,24 )

it has zeros at ( -2,0) , even multiplicity since the graph touches the x axis at -2

and ( 2,0 ) odd multiplicity since the graph crosses the x axis at x = 2

so , equation would be of the form

y = a ( x+ 2)^2 ( x- 2)

finding the value of a

24 = a ( 0+2)^2 (0-2)

24 = -8a

a = -3

hence, the function is

y = -3 ( x+2)^2 (x-2)

y = -3x^3 - 6x^2 +12x + 24

2) e^(t-4) ( t+9)

e^(t-4) = e^t / e^4

e^(t-4) ( t+9)

= e^t ( t+9) / e^4