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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.
What determines if a quadratic function has no x-intercepts?
If the quadratic function is written as ax2 + bx + c, then it has no x-intercepts if the discriminant, (b2 - 4ac), is negative.
How do you know if a quadratic function is factorrable or not?
If its discriminant is less than zero it can't be factored.
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.
How do you find the discriminant of a function?
To find the discriminant of a quadratic function, first express it in descending powers, thusax^2 + bx + c = 0 where a, b and c are real and a is non-zero.Then the discriminant is b^2 - 4ac
How many discriminant did this quadratic equation have -4j2 3j-280?
A quadratic equation has one discriminant.
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.
How many times will the graph of a quadratic function cross or touch the x axis if the discriminant is zero?
Once.
What are quadratic equations with real roots?
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no 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.
What is the definition of quadratic discriminant?
The discriminant of the quadratic equation: y = ax^2 + bx + c is b^2 - 4ac
What a short example of a maximum of quadratic function?
A quadratic of the form ax2 + bx + c has no maximum if a > 0: it gets infinitely large. If a = 0 then it is not a quadratic. If a < 0 then the quadratic does have a maximum, and it is -D/4a where D is the discriminant = b2 - 4ac
How can you have one solution in something that is quadratic?
b^2 - 4ac, the discriminant will tell you that a quadratic equation may have one real solution( discriminant = 0 ) , two real solutions( discriminant > 0 ), or no real solutions( discriminant < 0 ).
