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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.

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

How are the discriminant and the graph of a quadratic equation related?

If the discriminant = 0 then the graph touches the x axis at one point If the discriminant &gt; 0 then the graph touches the x axis at two ponits If the discriminant &lt; 0 then the graph does not meet the x axis


If the discriminant is negative the graph of a quadratic function will cross or touch the x-axis time s?

If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.


How many times will a graph with a negative discriminant touch the y-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.


What does the discriminant tell you about the graph?

Whether the graph has 0, 1 or 2 points at which it crosses (touches) the x-axis.


Given the function below what is the value of the discriminant and how many times does the graph of this function intersect or touch the x-axis?

Discriminant = 116; Graph crosses the x-axis two times


When the discriminant is negative will the graph of the function cross or touch?

The graph will cross the y-axis once but will not cross or touch the x-axis.


What does a quadratic equation graph have with a negative discriminant?

It has a complete lack of any x-intercepts.


Using the discriminant how many times does the graph of this equation cross the x axis 3x2 plus 6x plus 20?

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


Find the discriminant for 2x2 - 3x - 5 0?

The discriminant is 49.


How do you find how many x intercepts the parabola has using the discriminant?

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


How many times will the graph of a quadratic function cross or touch the x axis if the discriminant is zero?

Once.


If the discriminant is zero the graph of a quadric function will cross or touch the x axis how many times?

It will touch it once.