1) A quadratic function has the following standard formula
y=ax²+bx +c
X intercepts are the roots, x_1= 12 and x_2=8
2) We can write any quadratic function having the roots and the coefficient of a
This way
y=a(x-x_1)(x- x_2) Plug into that the roots
y=a(x-12)(x-8) And the x and the y-coordinate of that point (9,5)
5=a(9-12)(9-8)
5=a(-3)(-1)
3a=5
a=5/3
3) Now we can write the function
y=5/3(x-12)(x-8)
y=5/3(x²-8x-12x+96)
y=5/3x² -100/3x +160
