SOLUTION: Based on the equations of the parabolas, identify each parabola whose focus and vertex lie in different quadrants. a. y=-x^2/8+x/4+23/8 b. y=x^2/32+x/4-13/2 c. x=-y^2/16-y/4+1

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Question 1180070: Based on the equations of the parabolas, identify each parabola whose focus and vertex lie in different quadrants.
a. y=-x^2/8+x/4+23/8
b. y=x^2/32+x/4-13/2
c. x=-y^2/16-y/4+11/4
d. x=y^2/16+y/4-19/4
e. x=-y^2/36-5y/18+299/36
f. y=-x^2/24-5x/12+95/24
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Based on the equations of the parabolas, identify each parabola whose focus and vertex lie in different quadrants.

a.

use vertex form

........complete square

......








=>, , =>
vertex is at (,)=(,)->Q I
focus is at: (,)=(,)=(,)->Q I
=>focus and vertex lie in quadrant

b.


.......






=>, , =>
vertex is at (,)=(,)->Q III
focus is at: (,)=(,)=(,)->Q II
=>focus and vertex lie in quadrants
c.

....






=>, , =>
vertex is at (,)=(,) ->Q VI
focus is at: (,)=(,)=(,) ->Q III
=>focus and vertex lie in quadrants


d.








=>, , =>
vertex is at (,)=(,) ->Q III
focus is at: (,)=(,)=(,) ->Q III
=>focus and vertex lie in quadrant


e.

.........





=>, , =>
vertex is at (,)=(,) ->Q IV
focus is at: (,)=(,)=(,) ->between Q III and Q IV
=>focus and vertex lie in quadrants


f.








=>,, =>
vertex is at (,)=(,)->Q II
focus is at: (,)=(,)=(,)->Q III
=>focus and vertex lie in quadrants
parabola whose focus and vertex lie in different quadrant: b,c,e, and f


Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Based on the equations of the parabolas, identify each parabola whose focus and vertex lie in different quadrants.
a. y=-x^2/8+x/4+23/8
b. y=x^2/32+x/4-13/2
c. x=-y^2/16-y/4+11/4
d. x=y^2/16+y/4-19/4
e. x=-y^2/36-5y/18+299/36
f. y=-x^2/24-5x/12+95/24
DEFINITELY not going to do all of those for you, JUST # 1.

If you like TORTURE, then you can do the problem the same way the other COMPLEX-PERSON who responded, did it! If you do not wish to TORTURE yourself, then read on.



 ------- Multiplying by LCD, 8



 ----- Complete the square on x by taking  of "b" on x, squaring it and ADDING it to both sides

 



Final equation, with a VERTICAL AXIS of SYMMETRY:  

                            Compare the above to: , where:  

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