Question

What is the focus of the parabola given by the equation y = x2 − 2x − 3?
Will give medal

Answer 1

Line is y = -1/2x + 4
Area is 7/3

You need to find the slope of the tangent line first. That is:
y' = 2x - 2 = 2(2) - 2 = 2

Perpendicular slope is then -1/2

y - 3 = -1/2(x - 2)
y = -1/2x + 4

Answer 2

Next you integrate, using the line as the upper bound, subtracting the lower bound parabola between 0 and 2 (first quadrant)

int(-1/2x + 4 - (x^2 - 2x + 3)) =
-1/4x^2 + 4x -x^3/3 + x^2 - 3x
Plug in 2 for x and you get

-1 + 8 - 8/3 + 4 - 6
12 - 29/3 = 7/3

Answer 3

@yumfumyum thank you

Answer 4

your welcome, can you help me

Answer 5

will give fan and medal

Answer 6

sure Ill try

Answer 7

i tagged you

Answer 8

@judyd94
If you are looking for the focus of the parabola, the answer should be an ordered pair in the form of (x,y).
For a parabola
\(y=a(x-h)^2+k\)
the focus is located at
F(h, k+1/(4a) )

You can express \(y=x^2-2x-3\) in the form \(y=a(x-h)^2+k\) by completing the square.

Answer 9

@mathmate would it be 1,5/14

Answer 10

1 is correct, since it is the axis of the parabola.
the other is not.
What do you have for k and a?

Answer 11

@mathmate I re worked it and got 1,-4