Question 257102: Decide on ANY ONE quadratic function of your choice whose graph will be a parabola. 1. Will your team's parabola open upwards or downwards?Why?
2. What’s the vertex of your team's parabola?
3. What’s the x-intercepts of your team's parabola?
4. Can you ever have parabolas that open to the left or which open to the right?Why?
Can someone please help me solvve this? I have submitted this question several times and no one has answered it. Thank you!!!
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! 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
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
If we apply the quadratic formula, we get in general,
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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:
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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.
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