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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.

 

 Nov 16, 2021
 #1
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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)- 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)- 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. 

 Nov 16, 2021

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