Write a quadratic relation in the form y = ax2 + bx + c with roots 4 and - 3 and passing through the point (3, -12).

y =  2*x^2 - 2*x - 24

Step-by-step explanation:

If we have a quadratic function with roots a and b, we can write the equation for that function as:

y = f(x) = A*(x - a)*(x - b)

Where A is the leading coefficient.

In this case, we know that the roots are: 4 and -3

Then the function will be something like:

f(x) = A*(x - 4)*(x - (-3) )

f(x) = A*(x - 4)*(x + 3)

Now we need to determine the value of A.

We also know that the graph of the function passes through the point (3, -12)

This means that:

f(3) = -12

Then:

-12 = A*(3 - 4)*(3 + 3)

-12 = A*(-1)*(6)

-12 = A*(-6)

-12/-6 = A

2 = A

Then the equation is:

y = f(x) = 2*(x - 4)*(x + 3)

Now we need to write this in standard form, so we just need to expand the equation:

y = f(x) = 2*(x^2 + x*3 - x*4 - 4*3)

y = f(x) = 2*(x^2 - x - 12)

y = f(x) = 2*x^2 - 2*x - 24

Then the relation is:

y =  2*x^2 - 2*x - 24