Answer:
Here you have it! Check the attachment :)
Step-by-step explanation:
Consider using WolframAlpha whenever you need a quick plot of a function!
I hope it helps :)
Represent any point on the curve by (x, 1-x^2). The distance between (0, 0) and (x, 1-x^2) is

To make this easier, let's minimize the SQUARE of this quantity because when the square root is minimal, its square will be minimal.
So minimize

Find the derivative of L and set it equal to zero.

This gives you

or

You can use the Second Derivative Test to figure out which value(s) produce the MINIMUM distance.

When x = 0, the second derivative is negative, indicating a relative maximum. When

, the second derivative is positive, indicating a relative MINIMUM.
The two points on the curve closest to the origin are
x=7-2t
Move 7 to the other side. Sign changes from +7 to -7.
x-7=7-7-2t
x-7=-2t
Divide by -2 for both sides
x/-2-7/-2=-2t/-2
x/2+7/2=t
Answer: t= x/2+7/2 or t=7/2+x/2