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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:

- x = (-b +- sqrt(b2 - 4ac)) / (2a).

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.

- (b2 - 4ac) > 0 : The square root will be a real number and the root of the equation will be two distinct real numbers, so the graph will cross the x-axis at two different points.
- (b2 - 4ac) = 0 : The square root will be zero and the roots of the equation will be a real number double root, so the graph will touch the x-axis at only one points.
- (b2 - 4ac) < 0 : The square root will be imaginary, and the roots of the equation will be two complex numbers, so the graph will not touch the x-axis.

So by looking at the graph, you can tell if the discriminant is positive, negative, or zero.

Q: How do you find the discriminant on a graph?

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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.

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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

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.

In this case, the discriminant is less than zero and the graph of this parabola lies above the x-axis. It never crosses.

The discriminant is 49.

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.

It will touch it once.