Given the vertex of a parabola is (-6, 8) and its focus is (-6, 10), find the equation.

Step-by-step explanation:

If you plot the vertex and the focus, you'll see that the focus is 2 units above the vertex. That tells us 2 things: first, that the parabola opens upwards and, second, that the value of p in our equation is 2 (since p is the number of units between the vertex and the focus). The equation is:

where h and k are the coordinates of the vertex and p is the number of units between the vertex and the focus. The vertex is given as (-6, 8), so h is -6 and k is 8. p is 2, so filling in we get:

which simplifies down to

Not sure in what form you need it, so I'll leave it like that and you may have to do some algebraic manipulation to get it into the form your teacher wants it in.

Andre has more money than Bob.  If Andre gave Bob $20, they would have the same amount.  While if Bob gave Andre $22, Andre would then have twice as much as Bob.  How much does each one actually have?

Step-by-step explanation:

Here is the first sentence:

"If Andre gave Bob $20, they would have the same amount."

Algebraically:

1)   x − 20 = y + 20.

(Andre -- x -- has the same amount as Bob, after he gives him $20.)

Here is the second sentence:

"While if Bob gave Andre $22, Andre would then have twice as much

as Bob."

Algebraically:

2)   x + 22 = 2(y − 22).

(Andre has twice as much as Bob -- after Bob gives him $22.)

To solve any system of two equations, we must reduce it to one equation in one of the unknowns.  In this example, we can solve equation 1) for x --

x − 20=y + 20

 implies  x=y + 40

-- and substitute it into equation 2):

y + 40 + 22=2(y − 22).

      That is,

y + 62=2y − 44,

y − 2y=− 44 − 62,

according to the techniques of Lesson 9,

−y=−106

y=106.

Bob has $106.  Therefore, according to the exression for x, Andre has

106 + 40 = $146.

I hope this helps u! :D