Find a possible formula for the quadratic function whose graph has x intercepts 4 and 8 and y intercept 26?

The x-intercepts are quite easy. Just write the equation:

y = (x - 4)(x - 8)

To get the desired y-intercept, you need to multiply this by a scale factor (a constant). Just calculate the y-intercept for the equation as shown above; that will show you by what constant you need to multiply (for example, if the y-intercept is 13, add a factor of 2, to get 26).