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The form of the quadratic is ax2+bx+c, so the discriminant is b2-4ac.

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Q: What is the discriminant of a quadratic function?
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Continue Learning about Algebra

Why does the discriminant determine the number and type of the solutions for a quadratic equation?

A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.


Could there be a quadratic function that has an undefined axis of symmetry?

Yes and this will happen when the discriminant of a quadratic equation is less than zero meaning it has no real roots.


If the discriminant of a quadratic equation is -4 how many solutions does the equation have?

If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.


How many times will The graph of a quadratic function crosses the x-axis twice?

A quadratic function will cross the x-axis twice, once, or zero times. How often, depends on the discriminant. If you write the equation in the form y = ax2 + bx + c, the so-called discriminant is the expression b2 - 4ac (it appears as part of the solution, when you solve the quadratic equation for "x" - the part under the radical sign). If the discriminant is positive, the x-axis is crossed twice; if it is zero, the x-axis is crossed once, and if the discriminant is negative, the x-axis is not crossed at all.


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

It will touch the x-axis and not cross it.