Properties of quadratic equations :
Here we are going to see the properties of quadratic equations which would be much useful to the students who practice problems on quadratic functions.
1. The zeros of a quadratic function f(x) = ax²+bx+c are nothing but the two values of "x" when f(x) = 0 or ax² + bx +c = 0.
"ax² + bx +c = 0" is called as quadratic equation
Finding the two zeros of a quadratic function or solving the quadratic equation are the same thing.
3. There are three methods to find the two zeros of a quadratic equations.
(ii) Quadratic formula
(iii) Completing square
4. If the two zeros of a quadratic equation are irrational, then the two zeros (roots) will occur in conjugate pairs. That is, if (m+√n)is a root, then (m-√n) is the other root of the same equation.
5. The sum of the zeros of the quadratic equation ax²+bx+c = 0 is -b/a
6. The product of the zeros of the quadratic equation ax²+bx+c = 0 is c/a
7. If one zero is reciprocal to the other root then their product c/a = 1 or c = a.
8. If one zero is equal to other root but opposite in sign then their -b/a = 0 or b = 0.
9. If we know the two roots of a quadratic equation, we can use the following formula to form the quadratic equation.
x² - (Sum of the roots)x + product of the roots = 0
10. The graph of any quadratic equation will be a parabola.
11. The zeros of a quadratic equation are the x-coordinates of the points where the parabola (graph of quadratic a function) cuts x-axis.
12. If the two zeros of a quadratic function are imaginary, then the graph (parabola) will never intersect x - axis.
13. The two x-intercepts of a parabola (graph of a quadratic function) are nothing but the zeros of the quadratic function.
14. x- coordinate of the vertex of the parabola is -b/2a and the vertex is [ -b/2a, f(-b/2a) ]
15. To know at where the parabola cuts y-axis or y-intercept of the parabola, we have to plug x = 0 in the given quadratic function.
16. f(x) = ax² + bx + c, if the sign of the first term (ax²) is negative, the parabola will be open downward. Otherwise, the parabola will be open downward.
17. The discriminant b² - 4ac discriminates the nature of the zeros of the quadratic equation ax² + bx + c = 0.
Let us see how this discriminant "b² - 4ac" can be used to know the nature of the roots of a quadratic equation.
After having gone through the stuff given above, we hope that the students would have understood "Properties of quadratic equations".
Apart from the stuff given above, if you want to know more about "Properties of quadratic-equations", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
MATH FOR KIDS
HCF and LCM word problems