ALGEBRA PARABOLAS

Question

Use the following information use find the equation in standard form, vertex, Axis of Symmetry, Focus, Directrix, which direction it opens, and the latus rectum.

SF: y= 1/20(x+2)^2−1

Answer 1

y= (1/20)(x+2)^2 -1

vertex is= (h,k) = ( -2,-1) axis of symmetry is x=h = -2

the parabola opens upwards, because 1/20 >0

focus is (-2, K+ a) where a=5, 4a = 10, where K = -1

focus = (-2, 4)

directrix is y=k-a, y= -1-5 =- 6

l

latus rectum = the distance of a line segment horizontally through the focus connecting points on the parabola

= distance from (7,4) to (-11,4) = 7+11 = 18