Question

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

a. (4,-15/4)
b. (1,4)
c. (1,-4)
d. (1,15/4)
e. (1,-15/4)

Answer 1

i swear i just saw this question a second ago

Answer 2

trick is to write it as
\[y+3=x^2-2x\] then complete the square on the left
do you know how to do that?

Answer 3

lol i mean on the RIGHT

Answer 4

no i dont :( @misty1212

Answer 5

ok ready? it is not hard

Answer 6

ready @misty1212

Answer 7

what is half of 2?

Answer 8

...

Answer 9

1 @misty1212

Answer 10

ok and \(1^2=1\) so we go right from
\[y+3=x^2-2x\] to
\[y+3+1=(x-1)^2\] or
\[y+4=(x-1)^2\]

Answer 11

now we need the focus, but first we need the vertex
the vertex we see from our eyeballs is \((1,-4)\)

Answer 12

then we compare to the standard form
\[4p(y-k)=(x-h)^2\] and see that in this case \(4p=1\)so \(p=\frac{1}{4}\)

Answer 13

so we travel \(\frac{1}{4}\) units up from \((1,-4)\) and get to \((1,-\frac{15}{4})\)

Answer 14

what to check it

Answer 15

yes please thank you @misty1212