Question

When a quadratic equation has one solution, there will be one x-intercept; when there are two solutions, there will be two x-intercepts and when the equation has no solution, the graph will have no x-intercepts",is there another way of determining this?

Answer 1

The statement is true, if you are talking about a graph of ax^2 + bc + c vs x, and if the equation you are trying to solve is
ax^2 + bx + c = 0

Another way of predicting the number of solutions is calculatin b^2 - 4ac. If it is zero there is one solution. If it is postive there are two. If it is negative there are none.

Answer 2

You are referring to the discriminant, which is part of the quadratic formula in the RADICAND section.

Here is how the discriminant works:

Given a quadratic equation in the forn
ax^2 + bx + c = 0, plug the coefficients into the expression
b^2 - 4ac to see what happens. The expression b^2 - 4ac is called the DISCRIMINANT and it is located in the RADICAND section of the quadratic formula.

1-If you get a positive number, the quadratic will have 2 unique solutions.

2-If you get ZERO, the quadratic will have exactly ONE solution, a double root.

3-If you get a negative number, the quadratic will have NO real solutions, just TWO imaginary ones. In other words, solutions will have the letter i, which is short for "imaginary number."

Is this clear?