## Finding the Equation of a Quadratic With Given Roots

If a quadratic equation has rootsandthenandare factors, sois also a factor. This completely defines the quadratic apart from a constant factor. Ifis this factor then the quadratic factorises asIf the quadratic has the single rootthe it must factorise as

We can findif we have the coordinates of some point on the curve.

Example: A quadratic equation has roots 1, 3 and passes through the pointFind the equation of the curve.

Because the roots are 1 and 3, the equation of the curve must be of the formSincelies on the curve, we must have

The equation of the quadratic is

Example: A quadratic equation has the single root 2 and passes through the pointFind the equation of the curve.

Because the root is 2 the equation of the curve must be of the formSincelies on the curve, we must have

The equation of the quadratic is

Example: A quadratic equation has the rootsandand passes through the pointFind the equation of the curve.

Because the roots areandthe equation of the curve must be of the formon expanding tge brackets. Sincelies on the curve, we must have

The equation of the quadratic is