1. Write a quadratic function in intercept form whose graph has the given x-intercepts and passes through the given point.

Question

x-intercepts: 2,3
point: (4,2)

2. Write a quadratic function in standard form whose graph passes through the given points.

(1,-2),(-2,1),(3,6)

Answer 1

first one is easy,
you know that x-2 and x-3 must be factors of the quadratic.
let the equation be
y = a(x-2)(x-3)
sub in (4,2) to solve for a, and you are done

the second takes a bit more work.
let the equation be
y = ax^2 + bx + c

now take each point and sub into that, giving you 3 equation in 3 unknowns.
first one:
-2 = a + b + c

take it from there.