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How to Solve Quadratic Equations

Quadratic equations are equations of the form ax2+bx+c=0 where a, b and c are real numbers. Educators are fond of asking their students about roots and the vertex of this equation. So to help students in solving these problems, listed below are some strategies that you can use. (Assume that the examples are solving the equation x2+3x+4=0, which implies that a=1; b=3 and c=4.)

 

By Graphing

By graphing the equation, we can see that the parabola is increasing and crosses the x-axis at two points which are (-1, 0) and (-3, 0). These two points are called the roots of the equations. Also, we can see that the equation has its vertex on the point (-3/2, 7/4).

 

 

By Quadratic formula

By using the quadratic formula which is x=(-b±√(b2-4ac))/2a, you can get the roots of the equation.

 

 

By Factoring

By factoring x2+3x +4 = 0, we can solve its roots. x2+3x+4 can be written as (x+3)(x+1)=0. Since the two terms are separated by multiplication, we can equate both sides to zero and by this you’ll get the two values of x.

 

 

By Completing the square

In completing the square, you will actually see a different type of equation or the standard form of the Quadratic equation. After completing the square, the example equation will turn out to be in the form y=a(x-h)2+k. This equation can help you easily solve for the vertex which is (h, k). Also, this equation can also help you find the axis of symmetry which is x=h.

 

MathComplete.Com hopes that it helped you find ways in solving quadratic equations. Frequent visits to MathComplete.Com can assure you of the best and easiest way to solve quadratic equations.