the point p is on the graph f(x)=x^2+2x+5 determine the distance from the point (-3,-2) to the point P as a function of x

Question

the point p is on the graph f(x)=x^2+2x+5 determine the distance from the point (-3,-2) to the point P as a function of x

Answer 1

y=x^2 +2x +5

distance from (-3,-2) to (x,y) is the distance from (-3,-2) to (x,x^2+2x+5)

= d(x) = [(x+3)^2 + (x^2+2x+5+2)^2]^(1/2)

use the distance formula, a version of the Pythagorean Theorem

d(x) = (x^2 +6x +9 +x^4 +4x^3 + 18x^2 + 28x + 49)^(1/2)

= (x^4+4x^3 +19x^2 +34x +58)^(1/2)