The range of the parabola shown in the graph is y>=-4 . If the equation y= ax^2+bx+c is used to represent the graph , what is the value of a ?
A) 1/3
B) 2/3
C) 3/2
D) 3

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Comments (3)

Here’s how I think about a question like this. The leading coefficient, a, tells us how quickly the parabola grows. Since all we care about is a, we can use the points you correctly calculated, and transpose them so that they’re easier to work with. If this parabola goes from a vertex of (6, –4) to (12, 8), that’s the same shape as a different parabola that goes from a vertex of (0, 0) to (6, 12). That parabola that goes from (0, 0) to (6, 12) will have the same leading coefficient, but it’ll have a much simpler equation overall: y = ax^2.

Plug (6, 12) into that equation to solve for a:

12 = a(6)^2
12 = 36a
1/3 = a

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