College Algebra & Trigonometry, 2018a

4.9. OPTIMIZATION 237
6
5
4
3
2
1
(x, y)
(5, 2)
−1 −1 1 2 3 4 5 6 7 8
−2
−3
−4
1) Using the distance formula d = √ (x 2 − x 1 ) 2 +(y 2 − y 1 ) 2 , we can say that
any point on the curve y = x 2 − 4 is a distance of:
d = √ (x − 5) 2 +(y − 2) 2
from the point (5, 2). Because the question asks for this to be expressed as a
function of x, we should replace the y variable with an equivalent expression
involving x.
d = √ (x − 5) 2 +(x 2 − 4 − 2) 2
or
d = √ (x − 5) 2 +(x 2 − 6) 2