



 
Hi Kenzie. It sounds like you are describing a parabola that opens upward, and indeed that is what the equation is. Here's how I would solve this problem. 1. I look at its shape and recognize it as a parabola. That means that I can write it in the following form:
If I can replace B, C and A with numbers, I will have the complete equation for the parabola. 2. The graph crosses the x axis when x = 2. So at that point, y = 0. That means one of the factors A, (x  B) or (x  C) must be zero. If A is zero, then y is always zero, so that's not it. So let's say x  B = 0. Since at this point, x = 2, we can write 2  B = 0. Therefore B = 2. 3. Using the same logic, x  C = 0 when x = 3. So 3  C = 0 and that means C = 3. Now I have y = A (x  2) (x  3) which is y = A (x + 2) (x  3). 4. I also know that the parabola passes through the vertex, whose coordinates are (0, 6). That means y = 6 when x = 0. So I'll substitute this into the equation:
Now I have the equation of the parabola, and I can multiply it out:
I hope this demonstration helps,  


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