Question

If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

Answer 1

Equations don't really have x intercepts, functions or curves do. They're also known as the zeros of the function.  When we set a function equal to zero we get an equation to solve, and the zeros of the function become the solutions or roots of the equation.

If a quadratic equation only has one root, that's a repeated root corresponding to a discriminant of zero.

In this example our equation is something like $2(x+3)^2=0$, or expanded

$2x^2+12x + 18 = 0$

The discriminant $d=b^2-4ac$ here is

$d = 12^2 - 4(2)(18) = 0 \quad\checkmark$