6. What is the minimum vertical distance between the parabolas y=x^(2)+1 \text { and } y=x-x^(2) ?

Question

6. What is the minimum vertical distance between the parabolas
`y=x^(2)+1 \text { and } y=x-x^(2) ?`

Answer 1

0.75.

Explanation:

1) the required vertical distance is the distance between two vertexes.

2) according to the item 1, the coordinates of the vertexes are:

(y=x²+1): x₀=0; y₀=1;

(y=x-x²): x₀=0.5; y₀=0.25;

3) according to the item 2, the distance between 1 and 0.25 is 0.75.