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Geometrically speaking, a parabola is defined as the set of points that are the same distance from a given point and a given line. The point is called the focus of the parabola and the line is called the directrix of the parabola. Suppose P is a parabola with focus (4,3) and directrix y=1 . The point (8,6) is on P because (8,6)  is 5 units away from both the focus and the directrix. If we write the equation whose graph is P in the form y=ax^2 + bx + c, then what is a*b*c ?

 Jul 15, 2019
 #1
avatar+19782 
+2

"The standard form is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p "

 

3= k+p         and     1 = k-p

add together to get    4 = 2k    k = 2  (and p =1)     vertex is then   h, k = 4,2

 

fill in the form

(x-4)^2 = 4(1)(y-2)    expand

x^2 -8x+16 = 4y-8    solve for y

y = 1/4 x^2 -2x +6         a * b * c = -3

 Jul 15, 2019
 #2
avatar+104712 
0

Nicely explained, EP.....

 

 

cool cool cool

CPhill  Jul 15, 2019
 #3
avatar+1196 
-1

I'm using aops and it says that -3 is wrong.

 Jul 15, 2019
 #4
avatar+791 
+4

aops does not always work for me so i do mine on paper or on a text formate like this forum so?

travisio  Jul 15, 2019
 #5
avatar+1196 
-1

so what should I do.

Logic  Jul 15, 2019
 #6
avatar+791 
+4

honestly i would go to google if i could

other than that i'm like you i'm stumped

travisio  Jul 15, 2019
 #7
avatar+1653 
0

Are you putting hw probs here so other people can answer it and so you can pass your class?

 

Just curious.

tommarvoloriddle  Jul 22, 2019

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