Question

Find a function y=ax^2+bx+c whose graph has an x-intercept of -1, a y-intercept of 1 and a tangent line with a slope of 3 at the y-intercept

Answer 1

ok well let's rewrite the info they're given.
you have the points (0,-1) and (1,0) and that f'(0) = 3
so you have, plugging in the first point, -1 = c
and plugging in the second point gives you a + b = 1

Answer 2

f'(x) = 2ax +b
f'(0) = b = 3
so a+ 3 = 1 and a = -2
did that make sense?