y = ax^2+ bx + 9 has x-intercepts at x = -3 and x = 1.

what is the value of a?
what is the value of b?
please help!!

2 answers

knowing the roots, you know that
a(x+3)(x-1) = ax^2+bx+9
a(x^2+2x-3) = ax^2+bx+9
2a = b
-3a = 9
alternate way:
f(x) = ax^2 + bx + 9
f(-3) = 9a - 3b + 9 = 0 , 3a - b = -3
f(1) = a + b = -9

add, 4a = -12
a = -3, mentally get b = -6