The quadratic formula is x=2a-b±b2−4ac,
where a,b, and c correspond with the values of a quadratic equation written in standard form, ax2+bx+c=0. It is derived by completing the square on the general standard form equation. The quadratic formula can be used to find solution(s) to quadratic equations.The solutions of a quadratic equation in the form ax2+bx+c=0 can be interpreted graphically as the zeros of the quadratic function y=ax2+bx+c.
If the function has two zeros, the equation ax2+bx+c=0 has two solutions, and if the function has one zero, the equation has one solution. If the function doesn't have any zeros, the equation is said to have no real solutions.In the quadratic formula, the term under the radical sign is called the discriminant.
It's possible to use the discriminant to determine the number of solutions a quadratic equation has. b2−4acb2−4acb2−4ac >0⇔2 real solutions =0⇔1 real solution <0⇔0 real solutions The solutions to a quadratic equation correspond to the zeros of the parabola.
Solve the equation using the quadratic formula. 2x2−4x+10=0