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2y^2-12y-17=x

Guest May 27, 2017
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2y^2-12y-17=x

 

This is a sideways parabola (because it is the y that is squared)

it opens out in the positive direction because   the number in front of the y^2 is positive (+2)

When y=0, x=-17

So it must have 2 real roots, if you sketch what I have said so far you will see why.

 

\(\triangle = b^2-4ac = 144-136=8\)

8 is not a perfect square so there are 2 irrational roots.

 

The axis of symmetry is   y=-b/2a = 12/4 = 3

 

So the roots, (y intercepts), are,    

 

\(x=\frac{--12\pm\sqrt8}{4}\\ x=\frac{12\pm2\sqrt2}{4}\\ x=\frac{6\pm\sqrt2}{2}\\ \text{So it is a sideways parabola that passes through}\\ (\frac{6+\sqrt2}{2},0),\;\;\;(\frac{6-\sqrt2}{2},0),\;\;\;and \;\;\;(-17,0)\)

 

At the vertex y=3 sub that in to get the value of x

 

https://www.desmos.com/calculator/nfphydmkgk

Melody  May 27, 2017

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