SOLUTION: Consider the parabola y=x^2 +4x-3. Find the equation of the directrix. One of the following is correct. Which one is correct? A) y=-7 B) y=-7.25 C) y=-8 D) y=-7.75

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Consider the parabola y=x^2 +4x-3. Find the equation of the directrix. One of the following is correct. Which one is correct? A) y=-7 B) y=-7.25 C) y=-8 D) y=-7.75      Log On


   

Question 1199102: Consider the parabola y=x^2 +4x-3. Find the equation of the directrix.
One of the following is correct. Which one is correct?
A) y=-7
B) y=-7.25
C) y=-8
D) y=-7.75
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


y=x%5E2%2B4x-3

Complete the square to put the equation in vertex form. Vertex form is

y=%281%2F%284p%29%29%28x-h%29%5E2%2Bk

The vertex is (h,k); p is the directed distance from the directrix to the vertex and from the vertex to the focus.

y=%28x%5E2%2B4x%2B4%29-3-4
y=%28x%2B2%29%5E2-7

The vertex is (-2,-7); 1/(4p) = 1, so p = 1/4.

The parabola opens upward, so the directrix is p units below the vertex: -7 - 1/4 = -7.25.

ANSWER B) y=-7.25