PART A
The equation of the parabola in vertex form is given by the formula,

where

is the vertex of the parabola.
We substitute these values to obtain,

The point, (3,6) lies on the parabola.
It must therefore satisfy its equation.




Hence the equation of the parabola in vertex form is

PART B
To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

This implies that

We expand to obtain,

This will give us,


This equation is now in the form,

where

This is the standard form
Answer:
E: 2.00 + 0.75 [ 2r]
Step-by-step explanation:
r represents the number of miles. For each 1/2 mile the taxi will charge and extra free of $0.75. Then, for each mile, the taxi will charge $0.75*2. For example:
For a trip of 1 mile the taxi will charge:
$2.00+$0.75*2
For a trip of 2 miles, the taxi will charge:
$2.00+0.75*4
For a trip of 10 miles, the taxi will charge:
$2.00+$0.75*20
Notice that the variable fee (the one that depends on the number of miles) is $0.75 times the double of miles. In each case the number of miles is multiplied by two. Then the correct answer is E: 2.00 + 0.75 [ 2r]
Answer:



Step-by-step explanation:

They wanted to complete the square so they took the thing in front of x and divided by 2 then squared. Whatever you add in, you must take out.

Now we are read to write that one part (the first three terms together) as a square:

I don't see this but what happens if we find a common denominator for those 2 terms after the square. (b/2a)^2=b^2/4a^2 so we need to multiply that one fraction by 4a/4a.

They put it in ( )

I'm going to go ahead and combine those fractions now:

I'm going to factor out a -1 in the second term ( the one in the second ( ) ):

Now I'm going to add (b^2-4ac)/(4a^2) on both sides:

I'm going to square root both sides to rid of the square on the x+b/(2a) part:


Now subtract b/(2a) on both sides:

Combine the fractions (they have the same denominator):

Because 0.09 is ten times as big as 0.009
Answer:
-5x^4+8x^3-2x+1
Step-by-step explanation: