Consider the quadratic function:
f(x) = x2 – 8x – 9

Vertex:
What is the vertex of the function?
(, )

Step-by-step explanation:

I'm not sure how you are finding this in class, but the easiest way by far is to use the expressions for h and k:

 and

(Just a fun fact:  Those expressions come from the quadratic formula that help us to factor a quadratic equation.)

Filling in for h:

 simplifies to

Filling in for k:

 which simplifies a bit to

 which simplifies a bit more to

The vertex, then, is (4, -25).

You would also find this if you completed the square.  But again, I'm not sure how you're solving for the vertex in class.

(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

black/brown

step-by-step explanation:

well, you see here, jamal was born to 2 parents, his mother who he lives with and his father who left at a young age and who happens to be younger than him. he stole cookies because he has to steal food due to the fact that he spends his government poverty checks on pot and women.