4. f(x) = 3x² – 21x² – 54x
zero
multiplicity
|
effect

x = 0 or x = -3

Step-by-step explanation:

Solve for x:

-54 x - 18 x^2 = 0

Hint: | Factor the left hand side.

Factor x and constant terms from the left hand side:

-18 x (x + 3) = 0

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by -18:

x (x + 3) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

x = 0 or x + 3 = 0

Hint: | Look at the second equation: Solve for x.

Subtract 3 from both sides:

 x = 0 or x = -3

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3