The graph of the equation y = Ax^2 + Bx + C , where are A, B, C integers, is shown below. Find A + B + C.
+592 you can approach this question multiple ways.
start by finding the equation of this graph. you can do this in vertex or factored form for ease:
y = a(x + 1)2 - 1 or y = a(x)(x + 2)
now pick a point and substitute it in to find the dilation factor, a.
(1, 3)
3 = a(1 + 1)2 - 1 or 3 = a(1)(1 + 2)
3 = 4a - 1 3 = 3a
4 = 4a a = 1
a = 1
y = 1(x + 1)2 - 1 y = 1x(x + 2)
y = (x + 1)2 - 1 y = x(x + 2)
now you just convert the equation into standard form by expanding:
y = (x + 1)2 - 1 or y = x(x + 2)
y = x2 + 2x + 1 - 1 y = x2 + 2x
y = x2 + 2x
therefore a + b + c = 1 + 2 + 0
= 3.
