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What is the focus of the parabola given by the equation y= x^2 - 2x - 3

User JonnyG
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1 Answer

6 votes

Answer:

Explanation:

We can best determine this by putting the quadratic into work (vertex) form by completing the square. Move the -3 over to the other side to get

x^2 - 2x = 3. Now take half the linear term, square it, and add it to both sides. Our linear term is 2. Half of 2 is 1, and 1 squared is 1, so we add that to both sides:

x^2 - 2x + 1 = 3 + 1 and do some simplifying to both sides. The left side is a perfect square binomial:

(x - 1)^2 = 4

Move the 4 back over to get the vertex form of the quadratic:

y = (x-1)^2 - 4

The "a" value is a 1. Since p is found using a, and the coordinates of the focal point are (h, k + p), we need the vertex and the value of a. Now we have both. The value of p is found in:


p=(1)/(4lal) (those are absolute value symbols), hence, our p value is 1/4.

The coordinates of the focal point are (1, -4 + 1/4) or (1, -15/4)

User Tal Joffe
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