The discriminant is the expression under the square root of the quadratic formula.
For a quadratic equation: f(x) = ax2 + bx + c = 0, can be solved by the quadratic formula:
So if you graph y = f(x) = ax2 + bx + c, then the values of x that solve [ f(x)=0 ] will yield y = 0. The discriminant (b2 - 4ac) will tell you something about the graph.
So by looking at the graph, you can tell if the discriminant is positive, negative, or zero.
If the discriminant = 0 then the graph touches the x axis at one point If the discriminant > 0 then the graph touches the x axis at two ponits If the discriminant < 0 then the graph does not meet the x axis
Whether the graph has 0, 1 or 2 points at which it crosses (touches) the x-axis.
Discriminant = 116; Graph crosses the x-axis two times
In this case, the discriminant is less than zero and the graph of this parabola lies above the x-axis. It never crosses.
It will cross the x-axis twice.
If the discriminant = 0 then the graph touches the x axis at one point If the discriminant > 0 then the graph touches the x axis at two ponits If the discriminant < 0 then the graph does not meet the x axis
To accurately describe the discriminant for the graph, one would need to examine the nature of the roots of the quadratic equation represented by the graph. If the graph intersects the x-axis at two distinct points, the discriminant is positive. If it touches the x-axis at one point, the discriminant is zero. If the graph does not intersect the x-axis at all, the discriminant is negative.
If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.
A graph of an equation in the form y = ax^2 + bx + c will cross the y-axis once - whatever its discriminant may be.
Whether the graph has 0, 1 or 2 points at which it crosses (touches) the x-axis.
Discriminant = 116; Graph crosses the x-axis two times
The graph will cross the y-axis once but will not cross or touch the x-axis.
It has a complete lack of any x-intercepts.
The discriminant is 49.
In this case, the discriminant is less than zero and the graph of this parabola lies above the x-axis. It never crosses.
If the discriminant is negative, there are 0 interceptsIf the discriminant is zero, there is 1 interceptIf the discriminant is positive, there are 2 intercepts
Once.