SOLUTION: Find the minimum distance between f(x)=x^2 and y=2x-5

Algebra.Com
Question 125671: Find the minimum distance between f(x)=x^2 and y=2x-5
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
let's first graph given parabola and a line


as you can see, there are no points of intersection
on a graph above we have given parabola and line
now, I will add a line parallel to the given line (these lines have same slopes) which will be a tangent (there will be one point of intersection) on parabola ; the distance between these two parallel lines will be equal to the distance between the given line and parabola



now, we can choose two points (one on each of parallel lines) and find a distance between them; it will be also equal to the distance between parabola and the given line

Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:



Thus in our case, the required distance is



For more on this concept, refer to Distance formula.




answer is: the distance is
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