Which is the graph of the quadratic equation that has a negative discriminant?
The graph of a quadratic equation that has a negative discriminant is the one that never intersect x-axis. The graph of a quadratic equation that has a zero discriminant is the one that intersect x-axis at only one point. To be clearer, it can be seen in the attached image.
Which graph of a quadratic equation that has a positive discriminant?
Remember, the solutions to a quadratic equation are often called roots or zeros. The roots/zeros/solutions are the the values for x that make the equation equal to 0. On a graph, this will be where the parabola crosses the x-axis. Anytime the discriminant is positive, the graph will cross the x-axis twice.
How many solutions does a quadratic equation have if it’s discriminant is negative?
Is the discriminant negative or positive?
A quadratic expression which always takes positive values is called positive definite, while one which always takes negative values is called negative definite. Quadratics of either type never take the value 0, and so their discriminant is negative.
How do you know if a quadratic equation has no solution?
If the discriminant is less than 0, the equation has no real solution. Looking at the graph of a quadratic equation, if the parabola does not cross or intersect the x-axis, then the equation has no real solution. And no real solution does not mean that there is no solution, but that the solutions are not real numbers.
How can you tell if a quadratic function is positive or negative?
However, when written in the form Ax^2+Bx+C=f(x), we can tell whether the parabola opens up or opens down by the sign of A. If A is positive, the parabola opens up. If A is negative, then it opens down.
How does the discriminant relate to a graph?
A positive value indicates two solutions, zero indicates one solution, and a negative value indicates no real solution. The value of the discriminant can also be used to find the number of x-intercepts of the graph of y ax2 bx c.
What is a repeated real number solution?
When the left side factors into two linear equations with the same solution, the quadratic equation is said to have a repeated solution. We also call this solution a root of multiplicity 2, or a double root. SOLVING BY THE SQUARE.
Which graph shows a quadratic function with a discriminant value of 0?
Which graph shows a quadratic function with a discriminant value of 0? On a coordinate plane, a parabola opens up.
What if the discriminant is negative?
The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.
What can the roots to a quadratic equation be called?
Roots of Quadratic Equations and the Quadratic Formula Roots are also called x-intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis.
Can a quadratic equation have 3 solutions?
Therefore, our assumption that a quadratic equation has three distinct real roots is wrong. Hence, every quadratic equation cannot have more than 2 roots. Note: If a condition in the form of a quadratic equation is satisfied by more than two values of the unknown then the condition represents an identity.
How many solutions if the discriminant is negative?
If the value of the discriminant is zero, the quadratic equation has one real solution. If the value of the discriminant is negative, the quadratic equation has no real solutions.
What is the nature of the roots if the discriminant is negative?
Answer: The nature of roots simply means the category in which the roots are falling upon. The roots may be imaginary, real, unequal or equal. If the discriminate is negative, the roots will be imaginary.