F ( x ) = x 2 − 4 x − 12

What is the vertex?

vertex; (2, -16)

Step-by-step explanation:

Complete the square of this quadratic equation. Completing the square is a process used to convert a quadratic equation in standard form, into vertex form. This process involved, grouping the linear and quadratic terms, then factor out the coefficient of the quadratic term. After doing so, one must add a term to the quadratic equation to make the grouped part of the quadratic equation a perfect square. Then one will balance the equation and simplify. The additive inverse of the constant term that is added two (x) is the x-coordinate of the vertex. The constant is the y-coordinate of the vertex.

(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

what is

step-by-step explanation: