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A) Graph the parabola. Use graph paper or sketch neatly on regular paper. The parabola must be hand drawn - no computer tools or graphing calculator. (2 points)B) Give the vertex of the parabola. (2 points)C) Give the focus of the parabola. (1 points)D) Give the directrix of the parabola. (1 points)E) Give the endpoints of the latus rectum. (2 points)

A Graph The Parabola Use Graph Paper Or Sketch Neatly On Regular Paper The Parabola Must Be Hand Drawn No Computer Tools Or Graphing Calculator 2 PointsB Give T class=

Sagot :

The given equation of the parabola is expressed as

(y + 2)^2 = 12(x - 1)

The first step is to graph the parabola. The graph is shown below

The standard equation of a parabola whose axis is parallel to the x axis is expressed as

(y - k)^2 = 4p(x - h)

where

h and k are the x and y coordiantes of the vertex

focus = (h + p, k)

directrix = x = h - p

By comparing the given equation with this equation, we can see that the axis of the parabola is parallel to the x axis

By comparing the equation with the standard form equation,

B) h = 1, k = - 2

vertex = (1, - 2)

C) 4p = 12

p = 12/4 = 3

focus = (1 + 3, - 2)

focus = (4, - 2)

D) The vertex is halfway between the focus and directrix. Thus, the directrix would be x = - 2

E) The lactus rectum is a line passing through the focus and touching the two ends of the curve. From the graph, endpoints of the lactus rectum are

(4, 5) and (4, - 8)

View image AnnsleighS453705
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