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