Question 257102
I will give you an answer. Here is the question:
1. Will your team's parabola open upwards or downwards? Why? 
ANSWER: First all parabolas have the general equation
{{{y = a(x-h)^2 + k}}}
where (h,k) is the vertex.
The open up / down part depends on the parabola you have chosen. If you choose a<0 it will open down. If you choose a > 0, it will open up. Why? with a > 0, you are generating positive numbers times squared numbers which are positive numbers. So they will increase as x increases. With a < 0, you are generating negative numbers times squared numbers which are positive numbers. So they will decrease as x increases.
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2. What’s the vertex of your team's parabola? 
ANSWER: The vertex of any parabola in general is (h,k)
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3. What’s the x-intercepts of your team's parabola? 
ANSWER: in order to find the x-intercepts, we need the general quadratic formula as
{{{Ax^2 + Bx + C = 0}}}
If we apply the quadratic formula, we get in general,
{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}
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4. Can you ever have parabolas that open to the left or which open to the right?Why? 
ANSWER: Yes, we can have these they are called sleeping parabolas. To get these, reverse the x and y variables as the following:
{{{x = a(y-k)^2 + h}}}
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EX: Y = -2(X - 4)^2 + 6
This will open down since the front number is -.
The vertex is (4,6)
x-intercepts are: 4 +-sqrt(3)
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Hope that answers your questions satisfactorily.