Question

Consider the parabola y = x^2. Find the point on the parabola that is closest to the point (3, 1).

Answer 1

this is the problem of finding the minima

closest to point, means MINIMUM distance from that point

Answer 2

let the point be (x,y)

distance between x,y and 3,1
will be given by ?

Answer 3

\[1=3^2\]

Answer 4

??

Answer 5

use the distance formula
Distance between points (x1,y1) and (x2,y2) is
\(\huge d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

Answer 6

uuu.....I'll have to put it in that order right?

Answer 7

order doesn't matter
x1 - x2 or x2 - x1
both are same

Answer 8

here,
x1 = x
y1 = y = x^2

x2 = 3
y2 = 1

Answer 9

So..what's next?

Answer 10

plug those in the distance formula

Answer 11

Ok...Give me a sec:)

Answer 12

\[d=\sqrt{(x-3)^2}+(x^2-1)\]

Answer 13

Right??

Answer 14

to simplify things, we can also minimize the square of distance = d^2
so that we could ignore the square root sign,

and your function just becomes
\(f(x) = (x-3)^2+ (x^2-1)^2\)

Answer 15

So, that's my final answer..right?

Answer 16

did you cancel out
square root and square for x^2-1 ??

\(\sqrt{a^2+b^2} \ne \sqrt {(a^2)} +b \)

Answer 17

Yes. I did!:)

Answer 18

that was not correct thing to do ....

and do you know how to minimize the function ?

Answer 19

My bad.. and no..I don't know..

Answer 20

whats the topic of this question ?

derivatives ?

Answer 21

What? I don't know what exactly you're asking for...

Answer 22

pre-calc, right ?
any sub-topic?
any similar solved question ?
so that i know which method to use to explain...

Answer 23

Hang on..I'm loosing connection real bad..As you can see....I'm replying late...so I'll just get back a little later.When it's better...

Answer 24

no problem :)

Answer 25

Ok. @hartnn Yes. It is Pre-calculus. No subtopic and I don't have any similar solved question yet..This is my first one...

Answer 26

PLEASE HELP!!
Complete the analogy below.
amplitude : loudness :: frequency : _________
A.

Answer 27

PLEASE HELP!!
Sound waves can best be described as _________.
A. opaque
B. polarized
C.

Answer 28

Which of the following major contributions were made by Maury?

creating navigati

Answer 29

Cousteau and Gagnan _____.

invented SCUBA
lived in Sealab II
developed u201csign

Answer 30

A scientist is studying the effect on human health of bacteria that live in the human intestine.

Answer 31

http://prntscr.com/kk56cx

Answer 32

Find the derivative dy/dx if

Answer 33

Alice wanted to compare birthday cake prices in two supermarkets. She wrote down the daily prices for a few days and found that the difference of the two sa

Answer 34

which of the following was directly caused by germanys invasion of Belgium

Answer 35

How do Hallyu2019s memories help advance the plot?

They suggest that Hally is afraid of his father.

Answer 36

math help pls

Answer 37

"If we fight the stranger, we shall hit our brothers and perhaps shed the blood of a clansman.

Answer 38

... help please? am i right?
http://prntscr.com/kjxchc

Answer 39

Solve.
33=8^5z+4

Answer 40

A car is moving southwest at a velocity of 10 meters per second. Five seconds later, it's going 40 meters per second.

Answer 41

If you run 10 km east and then turn around and run 7 km west, how much total distance have you travelled?
A.

Answer 42

Which of the following is a vector measurement?
A. 0.08 g/L
B. 6.5 m/s down
C. 45 m/s slowly
D. 15 km/hr

Answer 43

The beginning of the Anglo-Saxon period roughly corresponds with which historical

Answer 44

What is the angle of rotation for the polygon shown?

https://learning.k12.com/content/enforced/437405-COF_ID125380/Picture2.

Answer 45

What type of transformation is shown in this image?

https://learning.k12.com/content/enforced/437405-COF_ID125380/Picture1.