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The entire graphs of the equation y=x^2+...

The entire graphs of the equation `y=x^2+kx-x+9` is strictly above the x-axis if and only if

A

`k lt 7`

B

`-5 lt k lt 7`

C

`k gt -5`

D

None of these

Text Solution

Verified by Experts

`y=x^(2) + (k-1)x+9= (x+ (k-1)/(2))^(2) + 9 - ((k-1)/(2))^(2)`
For the entire graph to be above the x-axis, we should have
`" "9- ((k-1)/(2))^(2) gt 0`
`rArr" "k^(2)-2k -35 lt 0 rArr (k=7)(k+5) lt 0`
`rArr -5 lt k lt 7`
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CENGAGE PUBLICATION-GRAPHS OF ELEMENTARY FUNCTIONS -EXERCISES
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  2. The following figure shows the graph of f(x) =ax^(2)+bx +c, then find ...

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  3. The entire graphs of the equation y=x^2+kx-x+9 is strictly above the x...

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  4. If x^2+2a x+a<0AAx in [1,2], the find the values of adot

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  5. Draw the graph of f(x) = x|x|.

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  6. Draw the graph of the function: Solve |(x^2)/(x-1)|lt=1 using the grap...

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  7. Draw the graph of y = |x^(2) - 2x|-x.

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  8. Draw the graph of y = {{:(2^(x)",",, x^(2)-2x le 0 ),( 1+3.5 x- x^(2),...

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  9. Draw the graph of f(x)= |2x-1|+ |2x-3|. Find the range of the function...

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  10. Draw the graph of f(x) =y= |x-1|+3|x-2|-5|x-4| and find the values of ...

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  11. Find the set of real value(s) of a for which the equation |2x+3|+2x-3|...

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  12. Draw the graph of y= 2^(((|x|+x))/(x)).

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  13. Draw the graph of y= x ^((1)/(log(e)x)).

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  14. Find the number of solutions to the equation x+log(e)x=0.

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  15. draw the graph of f(x)=x+[x], [.] denotes greatest integer function.

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  16. Given f(x) is a periodic function with period 2 and it is defined as ...

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  17. Draw the region of relation [x][y]= 6, x, y ge 0. Here [*] denotes the...

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  18. lim(xrarrc)f(x) does not exist for wher [.] represent greatest integ...

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  19. Let f(x) = ([x]+1)/({x}+1) for f: [0, (5)/(2) ) to ((1)/(2) , 3], whe...

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  20. Draw the graph of y= 2^({x}), where {*} represents the fractional part...

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