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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.
What is the definition of quadratic discriminant?
The discriminant of the quadratic equation: y = ax^2 + bx + c is b^2 - 4ac
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 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 ).
