If x=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the
equation?
the discriminant is 0.
the discriminant is 6.
the discriminant is positive
the discriminant is negative
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The discriminant is 0

Step-by-step explanation:

In a quadratic equation , we use the quadratic formula to find the solutions

 x = (-b ± √(b2 - 4ac)) / 2a

 where a, b, and c are coefficients of the equation

 ax2 + bx + c = 0

 Since x=6 is the only x-intercept, the equation would be

 (x - 6)(x - 6) = 0

 Expanding this out, we get

 x2 - 12x + 36 = 0

 In this equation,

 a = 1

b = -12

c = 36

 Now the discriminant is the square-root part of the formula:

 b2 - 4ac

 Now plug in the values of a,b, and c into the discriminant.  

(-12)2 - 4(1)(36) = 144 - 144 = 0

 This number is under the square-root. The square-root of 0 is 0.