Graphing parabolas

Question

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The graph of the equation y = Ax^2 + Bx + C , where are A, B, C integers, is shown below. Find A + B + C.

Guest Jul 29, 2022

BuilderBoi · Answer 1 · 2022-07-29T07:43:47

When $x = 0$ , $y = 0x + 0x + 7 = 7$ , meaning $c = 7$

Likewise, when $x = 6$ , $y = 36a + 6b + 7 = 7$ , meaning $36a + 6b = 0$

When $x = 3$ , $y = 9a + 3b + 7 = 1$ , meaning $9a + 3b = -6$

So now, we have this system, and we need to solve for a and b:

$9a + 3b = -6$

$36a + 6b = 0$