SOLUTION: Hi, I have a few questions I'm having an extremely hard time figuring this out. 1. Find the vertex and intercepts of the parabola y=-3x^2+6 2. Solve the inequality, state

Algebra ->  Rational-functions -> SOLUTION: Hi, I have a few questions I'm having an extremely hard time figuring this out. 1. Find the vertex and intercepts of the parabola y=-3x^2+6 2. Solve the inequality, state      Log On


   

Question 314772: Hi, I have a few questions I'm having an extremely hard time figuring this out.
1. Find the vertex and intercepts of the parabola y=-3x^2+6
2. Solve the inequality, state the solution using the interval notation and graph it. x-3/x+5<0.
These are both for Math 209. Thank you so much for your time and help.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The parabola is already in vertex form,
y=a%28x-h%29%5E2%2Bk
where (h,k) is the vertex.
It's just a bit hidden.
y=-3x%5E2%2B6
y=-3%28x-0%29%5E2%2B6
The vertex is (0,6).
+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+10%2C+-3x%5E2%2B6%29+
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.
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x-3/x+5<0.
Break up the number line into 3 regions.
Region 1: (-infinity,-5)
Region 2: (-5,3)
Region 3: (3,infinity)
For each region, choose a point (not an endpoint) and test the inequality.
If the inequality is solved, that region is part of the solution.
.
.
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Region 1: x=-10
%28x-3%29%2F%28x%2B5%29%3C0
%28-10-3%29%2F%28-10%2B5%29%3C0
%28-13%29%2F%28-5%29%3C0
13%2F5%3C0
False, this region is not part of the solution.
.
.
.
Region 2: x=0
%28x-3%29%2F%28x%2B5%29%3C0
%280-3%29%2F%280%2B5%29%3C0
-3%2F5%3C0
True, this region is part of the solution.
.
.
.
Region 3: x=5
%28x-3%29%2F%28x%2B5%29%3C0
%285-3%29%2F%285%2B5%29%3C0
2%2F10%3C0
False, this region is not part of the solution.
.
.
.
Only Region 2 is the solution region.
(-5,3)
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.
.

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.
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The curve is below the x-axis(< 0) on in the region (-5,3).