SOLUTION: Hi Can I have some help with this problem? Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts. y=2x^2 + x-6

Algebra ->  Equations -> SOLUTION: Hi Can I have some help with this problem? Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts. y=2x^2 + x-6      Log On


   

Question 127522: Hi Can I have some help with this problem?
Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts.
y=2x^2 + x-6
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+600%2C+600%2C+-6%2C+6%2C+-10%2C+10%2C+2x%5E2+%2B+x+-+6%29+
y+=+2x%5E2+%2B+x+-+6
The y-intercept occurs where x+=+0
2%2A0%5E2+%2B+0+-+6+=+-6
(0,-6) is the y-intercept
The x-intercepts (the roots) occur where y+=+0
y+=+2x%5E2+%2B+x+-+6
2x%5E2+%2B+x+-+6+=+0
%282x+-+3%29%28x+%2B+2%29
The x-intercepts occur where
2x+-+3+=+0
2x+=+3
x+=+3%2F2
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x+%2B+2+=+0
x+=+-2
The x-intercepts occur at (3/2,0) and (-2,0)
----------------
The vertex occurs exactly between the roots
To find it, use v+=+%28r%5B1%5D+%2B+r%5B2%5D%29%29+%2F+2
%283%2F2+%2B+%28-2%29%29+%2F+2+=+-%281%2F4%29
The vertex is at (-1/4,y)