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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.
