Answers:
a = 3
b = 3
c = -6
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Explanation:
The roots are x = 1 and x = -2. This leads to the factors x-1 and x+2 respectively.
This is because something like x = 1 becomes x-1 = 0 after subtracting 1 from both sides. For x = -2, we add 2 to both sides getting x+2 = 0.
The factorization is y = a(x-1)(x+2)
Plug in (x,y) = (2,12) and solve for 'a'
y = a(x-1)(x+2)
12 = a(2-1)(2+2)
12 = a(1)(4)
12 = 4a
12/4 = a
3 = a
a = 3
So we have y = a(x-1)(x+2) update to y = 3(x-1)(x+2)
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The last thing we need to do is expand everything out (use the FOIL rule then distributive rule) to get the equation into standard form
y = 3(x-1)(x+2)
y = 3(x^2+2x-1x-2)
y = 3(x^2+x-2)
y = 3x^2+3x-6
Comparing this to y = ax^2+bx+c shows that:
a = 3
b = 3
c = -6
The graph is below.
