SOLUTION: graph Y=3x^2-8x+2 and give the vertex, domain and rage thanks 4 your time

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Question 62265: graph Y=3x^2-8x+2 and give the vertex, domain and rage
thanks 4 your time
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
graph Y=3x^2-8x+2 and give the vertex, domain and rage
This quadratic equation is in standard form: y=ax%5E2%2Bbx%2Bc
Your a=3, b=-8, c=2
We can find the x coordinate for the vertex with the formual highlight%28x=-b%2F2a%29
x=-%28-8%29%2F%282%283%29%29
x=8%2F6
x=4%2F3
Plug x=4/3 into your equation to find the y-coordinate of the vertex.
y=3%284%2F3%29%5E2-8%284%2F3%29%2B2
y=3%2816%2F9%29-32%2F3%2B2
y=16%2F3-32%2F3%2B2
y=16%2F3-32%2F3%2B6%2F3
y=%2816-32%2B6%29%2F3
y=-10%2F3
The vertex is (4/3,-10/3)
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The domain (possible x values) for all quadratic equations like this is ALL REAL NUMBERS. (x can be anything.) In set builder notation {x|x=R}, in interval notation (-infinity,infinity).
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The range (possible y values) is found by first looking at a. a=3--it is positive. That means that the parabola opens upward and the y coordinate of the vertex is it's lowest y. Therefore the range is {y|y>=-10/3}.
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Happy Calculating!!!