Four times the square of a number is thirty-six

The function is  1/4x^2  + x - 8

Step-by-step explanation:

In Factor form the function  is

a(x + 8)(x - 4)    where a is a constant to be found.

= a( x^2 + 4x - 32)  Note the coefficient of x is positive because the function has a minimum value.

The line of symmetry is x = (-8+4)/2 = -2.

So the minimum value  will be the  value of f(x) when x = -2, so we have the equation

a(-2+8)(-2-4) = -9

-36a = -9

a = 1/4.