# 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...

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

lemjay | High School Teacher | (Level 3) Senior Educator

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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.