Let p(x,y) be a point on the graph of y= X^2-3

Question

A) Express the distance from P to the point (1,2) as a function of x. Simplify completely.

B) Use your calculator to determine which value of x-yields the smallest d.

Answer 1

d = √[(x-1)^2 + (y-2)^2]
= √[(x-1)^2 + (x^2-3-2)^2]
= √(x^2-2x+1 + x^4-10x^2+25)
= √(x^4-9x^2-2x+26)

Answer 2

Square root of x^4-5x^2+9