Question

Write a formula for the distance between a point (x, y) on the graph of y = x^4 and the point (3, 6). Express your answer in terms of x.

Answer 1

distance between points (3, 6) an (x, x^4) is done with the distance formula:

Distance = \(\large \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \)

Answer 2

so plug in your x coordinates of 3 and x and your y coordinates of 6 and x^4 into the formula...

Answer 3

But how would you get anything from the x^4? Thats what I'm confused about.

Answer 4

the point (x, x^4) is on the graph of y = x^4... didn't you say you wanted an expression (in terms of x) for the distance between (3, 6) and a point on the graph?

Answer 5

yes.

Answer 6

What do I do after I plugged the points in the distance formula? How do I get the answer?

Answer 7

I have square root of (3-x)^2 + (6-x^4)^2

Answer 8

that's the expression for the distance between (3, 6) and a point on the graph for whatever value x has....

Answer 9

for example..
when x=2, the point (2, 2^4) or (2, 16) is on the graph of y=x^4....
so the distance between (3, 6) and (2, 16) is:

D = \(\large \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}=\sqrt{(3-2)^2+(6-16)^2} \)

Answer 10

So you are saying that that's my expresstion is the distance formula?

Answer 11

basically... yes....

Answer 12

but make it in terms of only x....

Answer 13

yes I got it. Thank you

Answer 14

yw...:)