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 ?

Logic Jul 15, 2019

#1**+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

ElectricPavlov Jul 15, 2019

#3

#4**+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

#6**+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**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