## Finding the Equation of a Quadratic With Given Roots

If a quadratic equation has roots and then and are factors, so is also a factor. This completely defines the quadratic apart from a constant factor. If is this factor then the quadratic factorises as If the quadratic has the single root the it must factorise as We can find if we have the coordinates of some point on the curve.

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

Because the roots are 1 and 3, the equation of the curve must be of the form Since lies 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 point Find the equation of the curve.

Because the root is 2 the equation of the curve must be of the form Since lies on the curve, we must have The equation of the quadratic is Example: A quadratic equation has the roots and and passes through the point Find the equation of the curve.

Because the roots are and the equation of the curve must be of the form on expanding tge brackets. Since lies on the curve, we must have The equation of the quadratic is 