First let's understand the discriminant. Discriminant is an equation of D = b²-4ac. Discriminant is to find how many solutions do the equation have. In case for Quadratic Equation, there are 3 types of solutions which are:
- No solutions or D < 0 — When D < 0, the equation does not have real roots.
- One solution or D = 0 — When D = 0, the equation has one real root.
- Two solutions or D > 0 — When D > 0, the equation has two real roots.
To find discriminant graphically, we need to know that the x-axis plane represents the solutions to the equations. All equations can be drawn as a graph. Some graphs do not intersect x-axis while some graph do.
- If a graph intersects x-axis, the equation for that graph has solutions.
- If a graph doesn't intersect x-axis, the equation doesn't have any real solutions.
You may also notice that some graphs intersect x-axis more than one point. Like I said that the x-axis represents the roots or the solutions. Intersecting x-axis "n" times means that the equation has "n" roots.
For example, if a graph intersects x-axis 8 points - the equation has 8 roots or solutions.
From the graph, the parabola intersects on x-axis just only one point. That means there is only one solution. The question asks to find the discriminant of the function. Recall that if D = 0, there's only one real root. Therefore the discriminant for the function is zero.
Answer
- The discriminant for function is zero.
Let me know if you have any doubts!
