Question 688478
{{{2x^2-5x-3>=0}}}
Where is the graph above the x axis?
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First
Find factors of 2 and 3 which can be subtracted to yield -5
Factors of 2: 1, 2
Factors of 3: 1, 3
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Adding -6 and 1 yields -5
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{{{(2x+1)(x-3)>=0}}}
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2x+1=0
2x = -1
{{{x=-1/2}}}
AND
x-3=0
{{{x=3}}}
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The line crosses at x = {{{-1/2}}} and 3.
Either below {{{-1/2}}}, between {{{-1/2}}} and 3, or above 3,
the graph is above the x axis.
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Being a positive quadratic, where the parabola forms a "smile,"
it is above the x axis where
{{{highlight_green(x<=-1/2)}}} AND {{{highlight_green(x>=3)}}}
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Between {{{-1/2}}} and 3, the parabola is below the x axis
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{{{graph(300,300,-10,10,-10,10,2x^2-5x-3)}}}
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