Rewrite the equation in vertex form by completing the square

f(x)=(3x-9)(x+1)

f(x) = 3(x - 1)² - 12

Step-by-step explanation:

Given

f(x) = (3x - 9)(x + 1) ← expand factors using FOIL

     = 3x² - 6x - 9

To complete the square the coefficient of the x² term must be 1

Factor 3 out of 3x² - 6x

f(x) = 3(x² - 2x) - 9

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 2x

f(x) = 3(x² + 2(- 1)x + 1 - 1) - 9

     = 3(x - 1)² - 3 - 9

     = 3(x - 1)² - 12 ← equation in vertex form

(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