Question

Let p = (x y) be a point on the graph of y=x^2-8.

a) express the distance d from P to the origin as a function of x
d) use graphing utility to graph d = d(x)
e) for what values of x is d smallest?

Answer 1

The function is: d(x) = √( x² + (x² - 8)²)

d) The graph is at the end.

e) the minimums are at x = -2.7, and x = 2.7

Let's find the distance:

For a point (x, y), the distance to the origin is given by:

d = √( x² + y²)

if (x, y) belongs to the parabola y = x² - 8, then we can replace y there, and we will get:

d = √( x² + (x² - 8)²)

This is the function d(x), you can see the graph of this function in the image at the end.

e) In the graph we can see that the minimum values of d are at:

x = -2.7

x = 2.7