SOLUTION: Consider the parabola y=x^2 +4x -3. Find the coordinates of the focus. The correct answer is one of the following. Which one is correct? A) (-2,-6.75) B) (2,6.75) C)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Consider the parabola y=x^2 +4x -3. Find the coordinates of the focus. The correct answer is one of the following. Which one is correct? A) (-2,-6.75) B) (2,6.75) C)       Log On


   

Question 1199101: Consider the parabola y=x^2 +4x -3.
Find the coordinates of the focus.
The correct answer is one of the following. Which one is correct?
A) (-2,-6.75)
B) (2,6.75)
C) (-2,-6)
D) (-2,-5.75)
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 focus is p units above the vertex: -7 + 1/4 = -6.75.

ANSWER A) (-2,-6.75)