Determine the equation of the quadratic with zeros x = 1 and x = 5 passing through the point (3,-12).

Please help

is the equation the quadratic as per the given conditions.

Step-by-step explanation:

Let the equation of the quadratic be:

Given that it has zeroes at x = 1 and x = 5 i.e. y = 0 at both the values of x.

Also passes through point (3, -12). i.e. when x = 3, y = -12

Putting x = 1, y = 0:

Putting x = 5, y = 0:

Putting x = 3, y = -12:

Equation (2) - Equation (1):

Equation (2) - Equation (3):

Equation (5) - Equation (4):

Putting value of a in equation (4):

Putting a and b in equation (1):

So, the quadratic equation is: