If a parabola has a vertex of (5,0) then this would indicate:
a) The Discriminant is > 0; 2 x intercepts
b) The Discriminant is = 0; 1 x intercept
c) The Discriminant is < 0; no x intercepts
d) The Discriminant would not exist
e) The Discriminant = 25
In a quadratic function y=ax^2+bx+c, the discriminant is used to determine number of solutions when y=0. Since the value of y is zero, it is the same as determining the number of x-intercepts.
So, if the discriminant is less than zero, there is no solution. Hence, no x-intercept.
If it is equal to zero, there is only one solution. So, the function has only one x-intercept.
And if it is greater than zero, there are two solutions. Thus, it has two x-intercepts.
Furthermore, a graph of quadratic function is a parabola. And in parabola, the point where in the y has only one corresponding value of x is the vertex.
So, at vertex (5,0) :
> There are no other value of x when y=0.
> Since the value of y is zero, it means that it is also the x-intercept of the quadratic function.
Hence, this parabola with vertex (5,0) indicates that its discriminant is equal zero and has one x-intercept.