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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.
What else can I help you with?
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 > 0 then the graph touches the x axis at two ponits If the discriminant < 0 then the graph does not meet the x axis
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
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.
How many times will the graph of a quadratic function cross or touch the x-axis if the discriminant is positive?
It will cross the x-axis twice.
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 > 0 then the graph touches the x axis at two ponits If the discriminant < 0 then the graph does not meet the x axis
What type of description is true of the discriminant for the graph below?
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 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.
Find the discriminant for 2x2 - 3x - 5 0?
The discriminant is 49.
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.
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.
