The graph of the quadratic function \(y=ax^2+bx+c:\)
- does not intersect the x-axis, when \(D=b^2-4ac<0;\)
- touches the x-axis at one point, when \(D=b^2-4ac=0;\)
- intersects x-axis at two points, when \(D=b^2-4ac>0.\)
For the function \(y=4x^2+20x+25,\) the discriminant D is
\(D=20^2-4\cdot 4\cdot 25=400-400=0.\)
This means that the graph of the function touches the x-axis at one point.
Since \(y=4x^2+20x+25=(2x+5)^2,\) then the tangent point has x-coordinate \(x=-2.5\) (value at which y=0).
Answer: correct choice is B
